Skip to main content

2013 | OriginalPaper | Buchkapitel

2. Origins and Generation of Long Memory

verfasst von : Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik

Erschienen in: Long-Memory Processes

Verlag: Springer Berlin Heidelberg

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter we discuss typical methods for constructing long-memory processes. Many models are motivated by probabilistic and statistical principles. On the other hand, sometimes one prefers to be lead by subject specific considerations. Typical for the first approach is the definition of linear processes with long memory, or fractional ARIMA models. Subject specific models have been developed for instance in physics, finance and network engineering. Often the occurrence of long memory is detected by nonspecific, purely statistical methods, and subject specific models are then developed to explain the phenomenon. For example, in economics aggregation is a possible reason for long-range dependence, in computer networks long memory may be due to certain distributional properties of interarrival times. Often long memory is also linked to fractal structures.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Abadir, K., & Talmain, G. (2002). Aggregation, persistence and volatility in a macro model. Review of Economic Studies, 69(4), 749–779. MATHCrossRef Abadir, K., & Talmain, G. (2002). Aggregation, persistence and volatility in a macro model. Review of Economic Studies, 69(4), 749–779. MATHCrossRef
Zurück zum Zitat Abete, T., de Candia, A., Lairez, D., & Coniglio, A. (2004). Percolation model for enzyme gel degradation. Physical Review Letters, 93, 228301. CrossRef Abete, T., de Candia, A., Lairez, D., & Coniglio, A. (2004). Percolation model for enzyme gel degradation. Physical Review Letters, 93, 228301. CrossRef
Zurück zum Zitat Abry, P., & Flandrin, P. (1994). On the initialization of the discrete wavelet transform. IEEE Signal Processing Letters, SPL-1(2), 32–34. CrossRef Abry, P., & Flandrin, P. (1994). On the initialization of the discrete wavelet transform. IEEE Signal Processing Letters, SPL-1(2), 32–34. CrossRef
Zurück zum Zitat Aharoni, A., & Feder, J. (1990). Fractals in physics. Amsterdam: North-Holland. Aharoni, A., & Feder, J. (1990). Fractals in physics. Amsterdam: North-Holland.
Zurück zum Zitat Andersen, T. G., & Bollerslev, T. (1997a). Heterogeneous information arrivals and return volatility dynamics: uncovering the long run in high frequency returns. Journal of Finance, 52, 975–1005. CrossRef Andersen, T. G., & Bollerslev, T. (1997a). Heterogeneous information arrivals and return volatility dynamics: uncovering the long run in high frequency returns. Journal of Finance, 52, 975–1005. CrossRef
Zurück zum Zitat Andersen, T. G., & Bollerslev, T. (1997b). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance, 4, 115–158. CrossRef Andersen, T. G., & Bollerslev, T. (1997b). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance, 4, 115–158. CrossRef
Zurück zum Zitat Anh, V. V., Angulo, J. M., & Ruiz-Medina, M. D. (1999). Possible long-range dependence in fractional random fields. Journal of Statistical Planning and Inference, 80(1–2), 95–110. MathSciNetMATHCrossRef Anh, V. V., Angulo, J. M., & Ruiz-Medina, M. D. (1999). Possible long-range dependence in fractional random fields. Journal of Statistical Planning and Inference, 80(1–2), 95–110. MathSciNetMATHCrossRef
Zurück zum Zitat Anh, V. V., Leonenko, N. N., & Shieh, N.-R. (2009). Multifractal products of stationary diffusion processes. Stochastic Analysis and Applications, 27(3), 475–499. MathSciNetMATHCrossRef Anh, V. V., Leonenko, N. N., & Shieh, N.-R. (2009). Multifractal products of stationary diffusion processes. Stochastic Analysis and Applications, 27(3), 475–499. MathSciNetMATHCrossRef
Zurück zum Zitat Arteche, J. (2004). Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models. Journal of Econometrics, 119(1), 131–154. MathSciNetCrossRef Arteche, J. (2004). Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models. Journal of Econometrics, 119(1), 131–154. MathSciNetCrossRef
Zurück zum Zitat Astrauskas, A., Levy, J., & Taqqu, M. S. (1991). The asymptotic dependence structure of the linear fractional Lévy motion. Lietuvos Matematikos Rinkinys (Lithuanian Mathematical Journal), 31, 1–28. MathSciNetMATH Astrauskas, A., Levy, J., & Taqqu, M. S. (1991). The asymptotic dependence structure of the linear fractional Lévy motion. Lietuvos Matematikos Rinkinys (Lithuanian Mathematical Journal), 31, 1–28. MathSciNetMATH
Zurück zum Zitat Avnir, D. (Ed.) (1989). The fractal approach to heterogeneous chemistry. New York: Wiley. Avnir, D. (Ed.) (1989). The fractal approach to heterogeneous chemistry. New York: Wiley.
Zurück zum Zitat Avram, F., & Taqqu, M. S. (1986). Weak convergence of moving averages with infinite variance. In E. Eberlein & M. S. Taqqu (Eds.), Dependence in probability and statistics (pp. 399–415). Boston: Birkhäuser. Avram, F., & Taqqu, M. S. (1986). Weak convergence of moving averages with infinite variance. In E. Eberlein & M. S. Taqqu (Eds.), Dependence in probability and statistics (pp. 399–415). Boston: Birkhäuser.
Zurück zum Zitat Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73, 5–59. MathSciNetMATHCrossRef Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73, 5–59. MathSciNetMATHCrossRef
Zurück zum Zitat Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996a). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74(1), 3–30. MathSciNetMATHCrossRef Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996a). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74(1), 3–30. MathSciNetMATHCrossRef
Zurück zum Zitat Baillie, R. T., Chung, C.-F., & Tieslau, M. A. (1996b). Analysing inflation by the fractionally integrated ARFIMA-GARCH model. Journal of Applied Econometrics, 11, 23–40. CrossRef Baillie, R. T., Chung, C.-F., & Tieslau, M. A. (1996b). Analysing inflation by the fractionally integrated ARFIMA-GARCH model. Journal of Applied Econometrics, 11, 23–40. CrossRef
Zurück zum Zitat Bak, P. (1996). How nature works: the science of self-organised criticality. New York: Copernicus Press. Bak, P. (1996). How nature works: the science of self-organised criticality. New York: Copernicus Press.
Zurück zum Zitat Barndorff-Nielsen, O. E., & Leonenko, N. N. (2005). Burgers’ turbulence problem with linear or quadratic external potential. Journal of Applied Probability, 42(2), 550–565. MathSciNetMATHCrossRef Barndorff-Nielsen, O. E., & Leonenko, N. N. (2005). Burgers’ turbulence problem with linear or quadratic external potential. Journal of Applied Probability, 42(2), 550–565. MathSciNetMATHCrossRef
Zurück zum Zitat Barndorff-Nielsen, O. E., & Shephard, N. (2001). Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society. Series B. Statistical Methodology, 63, 167–241. MathSciNetMATHCrossRef Barndorff-Nielsen, O. E., & Shephard, N. (2001). Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society. Series B. Statistical Methodology, 63, 167–241. MathSciNetMATHCrossRef
Zurück zum Zitat Barndorff-Nielsen, O. E., & Stelzer, R. (2011b). Multivariate supOU processes. The Annals of Applied Probability, 21(1), 140–182. MathSciNetMATHCrossRef Barndorff-Nielsen, O. E., & Stelzer, R. (2011b). Multivariate supOU processes. The Annals of Applied Probability, 21(1), 140–182. MathSciNetMATHCrossRef
Zurück zum Zitat Barndorff-Nielsen, O. E., Jensen, J. L., & Sørensen, M. M. (1998). Some stationary processes in discrete and continuous time. Advances in Applied Probability, 30(4), 989–1007. MathSciNetMATHCrossRef Barndorff-Nielsen, O. E., Jensen, J. L., & Sørensen, M. M. (1998). Some stationary processes in discrete and continuous time. Advances in Applied Probability, 30(4), 989–1007. MathSciNetMATHCrossRef
Zurück zum Zitat Barnsley, M. F. (1993). Fractals everywhere (2nd ed.). Boston: Academic Press. MATH Barnsley, M. F. (1993). Fractals everywhere (2nd ed.). Boston: Academic Press. MATH
Zurück zum Zitat Batchelor, G. K. (1953). The theory of homogeneous turbulence. Cambridge science classics. MATH Batchelor, G. K. (1953). The theory of homogeneous turbulence. Cambridge science classics. MATH
Zurück zum Zitat Bauwens, L., & Hautsch, N. (2009). Modelling financial high frequency data using point processes. In T. Mikosch, J.-P. Kreiss, R. A. Davis, & T. G. Andersen (Eds.), Handbook of financial time series (pp. 953–979). Berlin: Springer. CrossRef Bauwens, L., & Hautsch, N. (2009). Modelling financial high frequency data using point processes. In T. Mikosch, J.-P. Kreiss, R. A. Davis, & T. G. Andersen (Eds.), Handbook of financial time series (pp. 953–979). Berlin: Springer. CrossRef
Zurück zum Zitat Bauwens, L., Pohlmeier, W., & Veredas, D. (2008). Editor’s introduction: recent developments in high frequency financial econometrics. In L. Bauwens, W. Pohlmeier, & D. Veredas (Eds.), High frequency financial econometrics. Studies in empirical economics (pp. 1–5). CrossRef Bauwens, L., Pohlmeier, W., & Veredas, D. (2008). Editor’s introduction: recent developments in high frequency financial econometrics. In L. Bauwens, W. Pohlmeier, & D. Veredas (Eds.), High frequency financial econometrics. Studies in empirical economics (pp. 1–5). CrossRef
Zurück zum Zitat Becker, K.-H., & Dörfler, M. (1989). Dynamical systems and fractals. Cambridge: Cambridge University Press. MATHCrossRef Becker, K.-H., & Dörfler, M. (1989). Dynamical systems and fractals. Cambridge: Cambridge University Press. MATHCrossRef
Zurück zum Zitat Bender, C. (2003a). An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter. Stochastic Processes and Their Applications, 104(1), 81–106. MathSciNetMATHCrossRef Bender, C. (2003a). An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter. Stochastic Processes and Their Applications, 104(1), 81–106. MathSciNetMATHCrossRef
Zurück zum Zitat Bender, C. (2003b). An S-transform approach to integration with respect to a fractional Brownian motion. Bernoulli, 9(6), 955–983. MathSciNetMATHCrossRef Bender, C. (2003b). An S-transform approach to integration with respect to a fractional Brownian motion. Bernoulli, 9(6), 955–983. MathSciNetMATHCrossRef
Zurück zum Zitat Bender, C., Sottinen, T., & Valkeila, E. (2007). Arbitrage with fractional Brownian motion? Theory of Stochastic Processes, 13(29), No. 1–2, 23–34. MathSciNet Bender, C., Sottinen, T., & Valkeila, E. (2007). Arbitrage with fractional Brownian motion? Theory of Stochastic Processes, 13(29), No. 1–2, 23–34. MathSciNet
Zurück zum Zitat Beran, J., & Feng, Y. (2007). Weighted averages and local polynomial estimation for fractional linear ARCH processes. Journal of Statistical Theory and Practice, 1(2), 149–166. MathSciNetMATHCrossRef Beran, J., & Feng, Y. (2007). Weighted averages and local polynomial estimation for fractional linear ARCH processes. Journal of Statistical Theory and Practice, 1(2), 149–166. MathSciNetMATHCrossRef
Zurück zum Zitat Beran, J., & Ocker, D. (2001). Volatility of stock market indices—an analysis based on SEMIFAR models. Journal of Business & Economic Statistics, 19(1), 103–116. MathSciNetCrossRef Beran, J., & Ocker, D. (2001). Volatility of stock market indices—an analysis based on SEMIFAR models. Journal of Business & Economic Statistics, 19(1), 103–116. MathSciNetCrossRef
Zurück zum Zitat Beran, J., & Schützner, M. (2009). On approximate pseudo maximum likelihood estimation for LARCH-processes. Bernoulli, 15(4), 1057–1081. MathSciNetMATHCrossRef Beran, J., & Schützner, M. (2009). On approximate pseudo maximum likelihood estimation for LARCH-processes. Bernoulli, 15(4), 1057–1081. MathSciNetMATHCrossRef
Zurück zum Zitat Beran, J., Sherman, R., Taqqu, M. S., & Willinger, W. (1995). Long-range dependence in variable-bit-rate video traffic. IEEE Transactions on Communications, 43(234), 1566–1579. CrossRef Beran, J., Sherman, R., Taqqu, M. S., & Willinger, W. (1995). Long-range dependence in variable-bit-rate video traffic. IEEE Transactions on Communications, 43(234), 1566–1579. CrossRef
Zurück zum Zitat Beran, J., Schützner, M., & Ghosh, S. (2010). From short to long memory: aggregation and estimation. Computational Statistics & Data Analysis, 54(11), 2432–2442. MathSciNetCrossRef Beran, J., Schützner, M., & Ghosh, S. (2010). From short to long memory: aggregation and estimation. Computational Statistics & Data Analysis, 54(11), 2432–2442. MathSciNetCrossRef
Zurück zum Zitat Beran, J., Das, B., & Schell, D. (2012). On robust tail index estimation for linear long-memory processes. Journal of Time Series Analysis, 33(3), 406–423. MathSciNetCrossRef Beran, J., Das, B., & Schell, D. (2012). On robust tail index estimation for linear long-memory processes. Journal of Time Series Analysis, 33(3), 406–423. MathSciNetCrossRef
Zurück zum Zitat Berger, N. (2002). Transience, recurrence and critical behavior for long-range percolation. Communications in Mathematical Physics, 236, 531–558. CrossRef Berger, N. (2002). Transience, recurrence and critical behavior for long-range percolation. Communications in Mathematical Physics, 236, 531–558. CrossRef
Zurück zum Zitat Berkes, I., & Horváth, L. (2003). Asymptotic results for long memory LARCH sequences. The Annals of Applied Probability, 13, 641–668. MathSciNetMATHCrossRef Berkes, I., & Horváth, L. (2003). Asymptotic results for long memory LARCH sequences. The Annals of Applied Probability, 13, 641–668. MathSciNetMATHCrossRef
Zurück zum Zitat Biagini, F., Hu, Y., Øksendal, B., & Zhang, T. (2008). Stochastic calculus for fractional Brownian motion and applications. Berlin: Springer. MATHCrossRef Biagini, F., Hu, Y., Øksendal, B., & Zhang, T. (2008). Stochastic calculus for fractional Brownian motion and applications. Berlin: Springer. MATHCrossRef
Zurück zum Zitat Birkhoff, G. D. (1931). Proof of the ergodic theorem. Proceedings of the National Academy of Sciences of the United States of America, 17, 656–660. CrossRef Birkhoff, G. D. (1931). Proof of the ergodic theorem. Proceedings of the National Academy of Sciences of the United States of America, 17, 656–660. CrossRef
Zurück zum Zitat Biskup, M. (2004). On the scaling of the chemical distance in long range percolation models. Annals of Probability, 32, 2938–2977. MathSciNetMATHCrossRef Biskup, M. (2004). On the scaling of the chemical distance in long range percolation models. Annals of Probability, 32, 2938–2977. MathSciNetMATHCrossRef
Zurück zum Zitat Bojdecki, T., Gorostiza, L. G., & Talarczyk, A. (2007). A long range dependence stable process and an infinite variance branching system. Annals of Probability, 35(2), 500–527. MathSciNetMATHCrossRef Bojdecki, T., Gorostiza, L. G., & Talarczyk, A. (2007). A long range dependence stable process and an infinite variance branching system. Annals of Probability, 35(2), 500–527. MathSciNetMATHCrossRef
Zurück zum Zitat Bollerslev, T., & Mikkelsen, H. O. (1996). Modeling and pricing long memory in stock market volatility. Journal of Econometrics, 73(1), 151–184. MathSciNetMATHCrossRef Bollerslev, T., & Mikkelsen, H. O. (1996). Modeling and pricing long memory in stock market volatility. Journal of Econometrics, 73(1), 151–184. MathSciNetMATHCrossRef
Zurück zum Zitat Bollerslev, T., & Mikkelsen, H. O. (1999). Long-term equity anticipation securities and stock market volatility dynamics. Journal of Econometrics, 92(1), 75–99. MathSciNetMATHCrossRef Bollerslev, T., & Mikkelsen, H. O. (1999). Long-term equity anticipation securities and stock market volatility dynamics. Journal of Econometrics, 92(1), 75–99. MathSciNetMATHCrossRef
Zurück zum Zitat Bollerslev, T., Sizova, N., & Tauchen, G. (2012). Volatility in equilibrium: asymmetries and dynamic dependencies. Review of Finance, 16(1), 31–80. MATHCrossRef Bollerslev, T., Sizova, N., & Tauchen, G. (2012). Volatility in equilibrium: asymmetries and dynamic dependencies. Review of Finance, 16(1), 31–80. MATHCrossRef
Zurück zum Zitat Bolthausen, E., Deuschel, J.-D., & Zeitouni, O. (1995). Entropic repulsion of the lattice free field. Communications in Mathematical Physics, 170(2), 417–443. MathSciNetMATHCrossRef Bolthausen, E., Deuschel, J.-D., & Zeitouni, O. (1995). Entropic repulsion of the lattice free field. Communications in Mathematical Physics, 170(2), 417–443. MathSciNetMATHCrossRef
Zurück zum Zitat Bougerol, P., & Picard, N. (1992). Stationarity of GARCH processes and of some nonnegative time series. Journal of Econometrics, 52, 115–127. MathSciNetMATHCrossRef Bougerol, P., & Picard, N. (1992). Stationarity of GARCH processes and of some nonnegative time series. Journal of Econometrics, 52, 115–127. MathSciNetMATHCrossRef
Zurück zum Zitat Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: forecasting and control. San Francisco: Holden Day. MATH Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: forecasting and control. San Francisco: Holden Day. MATH
Zurück zum Zitat Bramson, M., Cox, J. T., & Durrett, R. (1996). Spatial models for species area curves. Annals of Probability, 24(4), 1727–1751. MathSciNetMATHCrossRef Bramson, M., Cox, J. T., & Durrett, R. (1996). Spatial models for species area curves. Annals of Probability, 24(4), 1727–1751. MathSciNetMATHCrossRef
Zurück zum Zitat Breidt, F. J., Crato, N., & de Lima, P. (1998). On the detection and estimation of long memory in stochastic volatility. Journal of Econometrics, 83, 325–348. MathSciNetMATHCrossRef Breidt, F. J., Crato, N., & de Lima, P. (1998). On the detection and estimation of long memory in stochastic volatility. Journal of Econometrics, 83, 325–348. MathSciNetMATHCrossRef
Zurück zum Zitat Brockwell, P. J., & Davis, R. A. (1991). Time series: theory and methods. Springer series in statistics. New York: Springer. CrossRef Brockwell, P. J., & Davis, R. A. (1991). Time series: theory and methods. Springer series in statistics. New York: Springer. CrossRef
Zurück zum Zitat Brockwell, P. J., & Marquardt, T. (2005). Lévy-driven and fractionally integrated ARMA processes with continuous-time parameter. Statistica Sinica, 15, 477–494. MathSciNetMATH Brockwell, P. J., & Marquardt, T. (2005). Lévy-driven and fractionally integrated ARMA processes with continuous-time parameter. Statistica Sinica, 15, 477–494. MathSciNetMATH
Zurück zum Zitat Brody, D. C., Syroka, J., & Zervos, M. (2002). Dynamical pricing of weather derivatives. Quantitative Finance, 2(3), 189–198. MathSciNetCrossRef Brody, D. C., Syroka, J., & Zervos, M. (2002). Dynamical pricing of weather derivatives. Quantitative Finance, 2(3), 189–198. MathSciNetCrossRef
Zurück zum Zitat Buchmann, B., & Klüppelberg, C. (2005). Maxima of stochastic processes driven by fractional Brownian motion. Advances in Applied Probability, 37(3), 743–764. MathSciNetMATHCrossRef Buchmann, B., & Klüppelberg, C. (2005). Maxima of stochastic processes driven by fractional Brownian motion. Advances in Applied Probability, 37(3), 743–764. MathSciNetMATHCrossRef
Zurück zum Zitat Buchmann, B., & Klüppelberg, C. (2006). Fractional integral equations and state space transforms. Bernoulli, 12(3), 431–456. MathSciNetMATHCrossRef Buchmann, B., & Klüppelberg, C. (2006). Fractional integral equations and state space transforms. Bernoulli, 12(3), 431–456. MathSciNetMATHCrossRef
Zurück zum Zitat Bunde, A. & Havlin, S. (Eds.) (1995). Fractals and disordered systems (2nd ed.). Berlin: Springer. Bunde, A. & Havlin, S. (Eds.) (1995). Fractals and disordered systems (2nd ed.). Berlin: Springer.
Zurück zum Zitat Cappé, O., Moulines, E., Pesquet, J.-C., Petropulu, A., & Yang, X. (2002). Long-range dependence and heavy-tail modeling for teletraffic data. IEEE Signal Processing Magazine, 19(3), 14–27. CrossRef Cappé, O., Moulines, E., Pesquet, J.-C., Petropulu, A., & Yang, X. (2002). Long-range dependence and heavy-tail modeling for teletraffic data. IEEE Signal Processing Magazine, 19(3), 14–27. CrossRef
Zurück zum Zitat Cassandro, M., & Jona-Lasinio, G. (1978). Critical point behaviour and probability theory. Advances in Physics, 27(6), 913–941. CrossRef Cassandro, M., & Jona-Lasinio, G. (1978). Critical point behaviour and probability theory. Advances in Physics, 27(6), 913–941. CrossRef
Zurück zum Zitat Chakrabarti, B. K., Bardhan, K. K., & Sen, A. K. (2009). Lecture notes in physics: Vol. 762. Quantum and semiclassical percolation and breakdown in disordered solids. Berlin: Springer. CrossRef Chakrabarti, B. K., Bardhan, K. K., & Sen, A. K. (2009). Lecture notes in physics: Vol. 762. Quantum and semiclassical percolation and breakdown in disordered solids. Berlin: Springer. CrossRef
Zurück zum Zitat Chambers, M. J. (1996). The estimation of continuous parameter long-memory time series models. Econometric Theory, 12, 374–390. MathSciNetCrossRef Chambers, M. J. (1996). The estimation of continuous parameter long-memory time series models. Econometric Theory, 12, 374–390. MathSciNetCrossRef
Zurück zum Zitat Chambers, M. J. (1998). Long memory and aggregation in macroeconometric time series. International Econometric Review, 39, 1053–1072. MathSciNetCrossRef Chambers, M. J. (1998). Long memory and aggregation in macroeconometric time series. International Econometric Review, 39, 1053–1072. MathSciNetCrossRef
Zurück zum Zitat Cheridito, P., Kawaguchi, H., & Maejima, M. (2003). Fractional Ornstein–Uhlenbeck processes. Electronic Journal of Probability, 8(3), 1–14. MathSciNet Cheridito, P., Kawaguchi, H., & Maejima, M. (2003). Fractional Ornstein–Uhlenbeck processes. Electronic Journal of Probability, 8(3), 1–14. MathSciNet
Zurück zum Zitat Chiriac, R., & Voev, V. (2010). Modelling and forecasting multivariate realized volatility. Journal of Applied Econometrics, 36(6), 922–947. MathSciNet Chiriac, R., & Voev, V. (2010). Modelling and forecasting multivariate realized volatility. Journal of Applied Econometrics, 36(6), 922–947. MathSciNet
Zurück zum Zitat Comte, F. (1996). Simulation and estimation of long memory continuous-time models. Journal of Time Series Analysis, 17(1), 19–36. MathSciNetMATHCrossRef Comte, F. (1996). Simulation and estimation of long memory continuous-time models. Journal of Time Series Analysis, 17(1), 19–36. MathSciNetMATHCrossRef
Zurück zum Zitat Coppersmith, D., Gamarnik, D., & Sviridenko, M. (2002). The diameter of a long-range percolation graph. Random Structures & Algorithms, 21, 1–13. MathSciNetMATHCrossRef Coppersmith, D., Gamarnik, D., & Sviridenko, M. (2002). The diameter of a long-range percolation graph. Random Structures & Algorithms, 21, 1–13. MathSciNetMATHCrossRef
Zurück zum Zitat Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Econometrics, 7(2), 174–196. MathSciNet Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Econometrics, 7(2), 174–196. MathSciNet
Zurück zum Zitat Cox, D. R., & Isham, V. (1980). Point processes. London: Chapman and Hall. MATH Cox, D. R., & Isham, V. (1980). Point processes. London: Chapman and Hall. MATH
Zurück zum Zitat Crato, N., & de Lima, P. J. (1993). Long-range dependence in the conditional variance of stock returns. Economics Letters, 25, 281–285. Crato, N., & de Lima, P. J. (1993). Long-range dependence in the conditional variance of stock returns. Economics Letters, 25, 281–285.
Zurück zum Zitat Crovella, M. E., & Bestavros, A. (1997). Self-similarity in world wide web traffic: evidence and possible causes. IEEE/ACM Transactions on Networking, 5(6), 835–846. CrossRef Crovella, M. E., & Bestavros, A. (1997). Self-similarity in world wide web traffic: evidence and possible causes. IEEE/ACM Transactions on Networking, 5(6), 835–846. CrossRef
Zurück zum Zitat Dacorogna, M., Muller, U., Nagler, R., Olsen, R., & Pictet, O. (1993). A geographical model for the daily and weekly seasoned volatility in the FX market. Journal of International Money and Finance, 12, 413–438. CrossRef Dacorogna, M., Muller, U., Nagler, R., Olsen, R., & Pictet, O. (1993). A geographical model for the daily and weekly seasoned volatility in the FX market. Journal of International Money and Finance, 12, 413–438. CrossRef
Zurück zum Zitat Daley, D. J. (1999). The Hurst index of long-range dependent renewal processes. The Annals of Probability, 27(4), 2035–2041. MathSciNetMATHCrossRef Daley, D. J. (1999). The Hurst index of long-range dependent renewal processes. The Annals of Probability, 27(4), 2035–2041. MathSciNetMATHCrossRef
Zurück zum Zitat Daley, D. J., & Vere-Jones, D. (1988). An introduction to the theory of point processes (1st ed.). New York: Springer. MATH Daley, D. J., & Vere-Jones, D. (1988). An introduction to the theory of point processes (1st ed.). New York: Springer. MATH
Zurück zum Zitat Daley, D. J., & Vere-Jones, D. (2007). An introduction to the theory of point processes (2nd ed.). New York: Springer. Daley, D. J., & Vere-Jones, D. (2007). An introduction to the theory of point processes (2nd ed.). New York: Springer.
Zurück zum Zitat Daley, D. J., & Vesilo, R. (1997). Long range dependence of point process with queueing examples. Stochastic Processes and Their Applications, 70, 265–282. MathSciNetMATHCrossRef Daley, D. J., & Vesilo, R. (1997). Long range dependence of point process with queueing examples. Stochastic Processes and Their Applications, 70, 265–282. MathSciNetMATHCrossRef
Zurück zum Zitat Daley, D. J., Rolski, T., & Vesilo, R. (2000). Long-range dependent point processes and their Palm–Khinchin distributions. Advances in Applied Probability, 32(4), 1051–1063. MathSciNetMATHCrossRef Daley, D. J., Rolski, T., & Vesilo, R. (2000). Long-range dependent point processes and their Palm–Khinchin distributions. Advances in Applied Probability, 32(4), 1051–1063. MathSciNetMATHCrossRef
Zurück zum Zitat Davidson, J., & Sibbertsen, P. (2005). Generating schemes for longmemory processes: regimes, aggregation and linearity. Journal of Econometrics, 128(2), 253–282. MathSciNetCrossRef Davidson, J., & Sibbertsen, P. (2005). Generating schemes for longmemory processes: regimes, aggregation and linearity. Journal of Econometrics, 128(2), 253–282. MathSciNetCrossRef
Zurück zum Zitat Davis, R. A., & Mikosch, T. (2001). Point process convergence of stochastic volatility processes with application to sample autocorrelations. Journal of Applied Probability, 38A, 93–104. MathSciNetMATHCrossRef Davis, R. A., & Mikosch, T. (2001). Point process convergence of stochastic volatility processes with application to sample autocorrelations. Journal of Applied Probability, 38A, 93–104. MathSciNetMATHCrossRef
Zurück zum Zitat Davis, R., & Resnick, S. (1985). Limit theory for moving averages of random variables with regularly varying tail probabilities. Annals of Probability, 13(1), 179–195. MathSciNetMATHCrossRef Davis, R., & Resnick, S. (1985). Limit theory for moving averages of random variables with regularly varying tail probabilities. Annals of Probability, 13(1), 179–195. MathSciNetMATHCrossRef
Zurück zum Zitat de Lima, B. N. B., & Sapozhnikov, A. (2008). On the truncated long-range percolation on \(\mathbb{Z}^{d}\). Journal of Applied Probability, 45(1), 287–291. MathSciNetMATHCrossRef de Lima, B. N. B., & Sapozhnikov, A. (2008). On the truncated long-range percolation on \(\mathbb{Z}^{d}\). Journal of Applied Probability, 45(1), 287–291. MathSciNetMATHCrossRef
Zurück zum Zitat Decreusefond, L., & Üstünel, A. S. (1999). Stochastic analysis of the fractional Brownian motion. Potential Analysis, 10, 177–214. MathSciNetMATHCrossRef Decreusefond, L., & Üstünel, A. S. (1999). Stochastic analysis of the fractional Brownian motion. Potential Analysis, 10, 177–214. MathSciNetMATHCrossRef
Zurück zum Zitat Deo, R., Hsieh, M.-C., Hurvich, C. M., & Soulier, P. (2006a). Long memory in nonlinear processes. In Lecture notes in statist.: Vol. 187. Dependence in probability and statistics (pp. 221–244). New York: Springer. CrossRef Deo, R., Hsieh, M.-C., Hurvich, C. M., & Soulier, P. (2006a). Long memory in nonlinear processes. In Lecture notes in statist.: Vol. 187. Dependence in probability and statistics (pp. 221–244). New York: Springer. CrossRef
Zurück zum Zitat Deo, R., Hurvich, C., & Lu, Y. (2006b). Forecasting realized volatility using a long-memory stochastic volatility. Journal of Econometrics, 131, 29–58. MathSciNetCrossRef Deo, R., Hurvich, C., & Lu, Y. (2006b). Forecasting realized volatility using a long-memory stochastic volatility. Journal of Econometrics, 131, 29–58. MathSciNetCrossRef
Zurück zum Zitat Deo, R., Hsieh, M.-C., & Hurvich, C. M. (2007). Long memory in intertrade durations, counts and realized volatility of NYSE stocks. Preprint. Deo, R., Hsieh, M.-C., & Hurvich, C. M. (2007). Long memory in intertrade durations, counts and realized volatility of NYSE stocks. Preprint.
Zurück zum Zitat Deo, R., Hurvich, C., Soulier, P., & Wang, Y. (2009). Conditions for the propagation of memory parameter from durations to counts and realized volatility. Econometric Theory, 25, 764–792. MathSciNetMATHCrossRef Deo, R., Hurvich, C., Soulier, P., & Wang, Y. (2009). Conditions for the propagation of memory parameter from durations to counts and realized volatility. Econometric Theory, 25, 764–792. MathSciNetMATHCrossRef
Zurück zum Zitat Ding, Z., & Granger, C. W. J. (1996). Modeling volatility persistence of speculative returns: a new approach. Journal of Econometrics, 73(1), 185–215. MathSciNetMATHCrossRef Ding, Z., & Granger, C. W. J. (1996). Modeling volatility persistence of speculative returns: a new approach. Journal of Econometrics, 73(1), 185–215. MathSciNetMATHCrossRef
Zurück zum Zitat Ding, Z., Granger, C., & Engle, R. (1993). A long-memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83–106. CrossRef Ding, Z., Granger, C., & Engle, R. (1993). A long-memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83–106. CrossRef
Zurück zum Zitat Dobrushin, R. L. (1965). Existence of a phase transition in two and three dimensional Ising models. Theory of Probability and Its Applications, 10, 193–213. MathSciNetMATHCrossRef Dobrushin, R. L. (1965). Existence of a phase transition in two and three dimensional Ising models. Theory of Probability and Its Applications, 10, 193–213. MathSciNetMATHCrossRef
Zurück zum Zitat Dobrushin, R. L. (1968a). Problem of uniqueness of a Gibbs random field and phase transitions. Functional Analysis and Applications, 2(4), 44–57 (in Russian). Dobrushin, R. L. (1968a). Problem of uniqueness of a Gibbs random field and phase transitions. Functional Analysis and Applications, 2(4), 44–57 (in Russian).
Zurück zum Zitat Dobrushin, R. L. (1968b). Gibbsian random fields for lattice systems with pairwise interactions. Funktsionalnyi Analiz I Ego Prilozheniya, 2(4), 31–43. [Funct. Anal. Appl., 2, 292–301 (1968)]. Dobrushin, R. L. (1968b). Gibbsian random fields for lattice systems with pairwise interactions. Funktsionalnyi Analiz I Ego Prilozheniya, 2(4), 31–43. [Funct. Anal. Appl., 2, 292–301 (1968)].
Zurück zum Zitat Dobrushin, R. L. (1968c). The description of a random field by means of conditional probabilities and conditions of its regularity. Teoriâ Veroâtnostej I Ee Primeneniâ, 13, 201–229. [Theor. Prob. Appl., 13, 197–224 (1968)]. Dobrushin, R. L. (1968c). The description of a random field by means of conditional probabilities and conditions of its regularity. Teoriâ Veroâtnostej I Ee Primeneniâ, 13, 201–229. [Theor. Prob. Appl., 13, 197–224 (1968)].
Zurück zum Zitat Dobrushin, R. L. (1969). Gibbs field: the general case. Functional Analysis and Applications, 3(1), 27–35 (in Russian). MathSciNet Dobrushin, R. L. (1969). Gibbs field: the general case. Functional Analysis and Applications, 3(1), 27–35 (in Russian). MathSciNet
Zurück zum Zitat Dobrushin, R. L. (1970). Prescribing a system of random variables by conditional distributions. Teoriâ Veroâtnostej I Ee Primeneniâ, 15, 469–497. [Theory Probab. Appl., 15, 458–486]. Dobrushin, R. L. (1970). Prescribing a system of random variables by conditional distributions. Teoriâ Veroâtnostej I Ee Primeneniâ, 15, 469–497. [Theory Probab. Appl., 15, 458–486].
Zurück zum Zitat Dobrushin, R. L. (1980). Gaussian random fields—Gibbsian point of view. In R. L. Dobrushin & Ya. G. Sinai (Eds.), Multicomponent random systems. Advances in probability and related topics (Vol. 6, pp. 119–152). New York: Dekker. Dobrushin, R. L. (1980). Gaussian random fields—Gibbsian point of view. In R. L. Dobrushin & Ya. G. Sinai (Eds.), Multicomponent random systems. Advances in probability and related topics (Vol. 6, pp. 119–152). New York: Dekker.
Zurück zum Zitat Domb, C. & Lebowitz, J. L. (Eds.) (2001). Phase transitions and critical phenomena (Vol. 18). San Diego: Academic Press. Domb, C. & Lebowitz, J. L. (Eds.) (2001). Phase transitions and critical phenomena (Vol. 18). San Diego: Academic Press.
Zurück zum Zitat Dombry, C., & Kaj, I. (2011). The on–off network traffic model under intermediate scaling. Queueing Systems, 69(1), 29–44. MathSciNetMATHCrossRef Dombry, C., & Kaj, I. (2011). The on–off network traffic model under intermediate scaling. Queueing Systems, 69(1), 29–44. MathSciNetMATHCrossRef
Zurück zum Zitat Douc, R., Roueff, F., & Soulier, P. (2008). On the existence of some processes. Stochastic Processes and Their Applications, 118(5), 755–761. MathSciNetMATHCrossRef Douc, R., Roueff, F., & Soulier, P. (2008). On the existence of some processes. Stochastic Processes and Their Applications, 118(5), 755–761. MathSciNetMATHCrossRef
Zurück zum Zitat Duncan, T. E., Hu, Y., & Pasik-Duncan, B. (2000). Stochastic calculus for fractional Brownian motion I. Theory. SIAM Journal on Control and Optimization, 38(2), 582–612. MathSciNetMATHCrossRef Duncan, T. E., Hu, Y., & Pasik-Duncan, B. (2000). Stochastic calculus for fractional Brownian motion I. Theory. SIAM Journal on Control and Optimization, 38(2), 582–612. MathSciNetMATHCrossRef
Zurück zum Zitat Durrett, R., & Levin, S. (1996). Spatial models for species-area curves. Journal of Theoretical Biology, 179(2), 119–127. CrossRef Durrett, R., & Levin, S. (1996). Spatial models for species-area curves. Journal of Theoretical Biology, 179(2), 119–127. CrossRef
Zurück zum Zitat Eberhard, J. W., & Horn, P. M. (1978). Excess 1/f noise in metals. Physical Reviews B, 18, 6681–6693. CrossRef Eberhard, J. W., & Horn, P. M. (1978). Excess 1/f noise in metals. Physical Reviews B, 18, 6681–6693. CrossRef
Zurück zum Zitat Elliott, R. J., & van der Hoek, J. (2003). A general fractional white noise theory and applications to finance. Mathematical Finance, 13, 301–330. MathSciNetMATHCrossRef Elliott, R. J., & van der Hoek, J. (2003). A general fractional white noise theory and applications to finance. Mathematical Finance, 13, 301–330. MathSciNetMATHCrossRef
Zurück zum Zitat Embrechts, P., & Maejima, M. (2002). Self-similar processes. Princeton: Princeton University Press. Embrechts, P., & Maejima, M. (2002). Self-similar processes. Princeton: Princeton University Press.
Zurück zum Zitat Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008. MathSciNetMATHCrossRef Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008. MathSciNetMATHCrossRef
Zurück zum Zitat Ercolani, J. S. (2011). On the asymptotic properties of a feasible estimator of the continuous time long memory parameter. Journal of Time Series Analysis, 32, 512–517. MathSciNetCrossRef Ercolani, J. S. (2011). On the asymptotic properties of a feasible estimator of the continuous time long memory parameter. Journal of Time Series Analysis, 32, 512–517. MathSciNetCrossRef
Zurück zum Zitat Falconer, K. (2003). Fractal geometry: mathematical foundations and applications (2nd ed.). Chichester: Wiley. MATHCrossRef Falconer, K. (2003). Fractal geometry: mathematical foundations and applications (2nd ed.). Chichester: Wiley. MATHCrossRef
Zurück zum Zitat Fasen, V., & Samorodnitsky, G. (2009). A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime. Advances in Applied Probability, 41(2), 393–427. MathSciNetMATHCrossRef Fasen, V., & Samorodnitsky, G. (2009). A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime. Advances in Applied Probability, 41(2), 393–427. MathSciNetMATHCrossRef
Zurück zum Zitat Faÿ, G., González-Arévalo, B., Mikosch, T., & Samorodnitsky, G. (2006). Modeling teletraffic arrivals by a Poisson cluster process. Queueing Systems, 54(2), 121–140. MathSciNetMATHCrossRef Faÿ, G., González-Arévalo, B., Mikosch, T., & Samorodnitsky, G. (2006). Modeling teletraffic arrivals by a Poisson cluster process. Queueing Systems, 54(2), 121–140. MathSciNetMATHCrossRef
Zurück zum Zitat Feller, W. (1971). An introduction to probability theory and its applications (Vol. 2). New York: Wiley. MATH Feller, W. (1971). An introduction to probability theory and its applications (Vol. 2). New York: Wiley. MATH
Zurück zum Zitat Fisher, M. E. (1964). Correlation functions and the critical region of simple fluids. Journal of Mathematical Physics, 5(7), 944–962. MathSciNetCrossRef Fisher, M. E. (1964). Correlation functions and the critical region of simple fluids. Journal of Mathematical Physics, 5(7), 944–962. MathSciNetCrossRef
Zurück zum Zitat Fleming, J., & Kirby, C. (2011). Long memory in volatility and trading volume. Journal of Banking & Finance, 35(7), 1714–1726. CrossRef Fleming, J., & Kirby, C. (2011). Long memory in volatility and trading volume. Journal of Banking & Finance, 35(7), 1714–1726. CrossRef
Zurück zum Zitat Föllmer, H. (1975). Phase transitions and Martin boundary. In Lecture notes in mathematics: Vol. 465. Sém. prob. IX (pp. 305–318). Berlin: Springer. Föllmer, H. (1975). Phase transitions and Martin boundary. In Lecture notes in mathematics: Vol. 465. Sém. prob. IX (pp. 305–318). Berlin: Springer.
Zurück zum Zitat Frisch, U. (1995). Turbulence: the legacy of A.N. Kolmogorov. Cambridge: Cambridge University Press. MATH Frisch, U. (1995). Turbulence: the legacy of A.N. Kolmogorov. Cambridge: Cambridge University Press. MATH
Zurück zum Zitat Fröhlich, J., & Spencer, T. (1982). The phase transition in the one-dimensional Ising model with 1/r 2 interaction energy. Communications in Mathematical Physics, 84(1), 167–170. CrossRef Fröhlich, J., & Spencer, T. (1982). The phase transition in the one-dimensional Ising model with 1/r 2 interaction energy. Communications in Mathematical Physics, 84(1), 167–170. CrossRef
Zurück zum Zitat Gaigalas, R. (2004). A non-Gaussian limit process with long-range dependence. Thesis Ph.D., Uppsala Universitet (Sweden). Gaigalas, R. (2004). A non-Gaussian limit process with long-range dependence. Thesis Ph.D., Uppsala Universitet (Sweden).
Zurück zum Zitat Gaigalas, R., & Kaj, I. (2003). Convergence of scaled renewal processes and a packet arrival model. Bernoulli, 9(4), 671–703 (English summary). MathSciNetMATHCrossRef Gaigalas, R., & Kaj, I. (2003). Convergence of scaled renewal processes and a packet arrival model. Bernoulli, 9(4), 671–703 (English summary). MathSciNetMATHCrossRef
Zurück zum Zitat Gao, J., & Rubin, I. (2001). Multiplicative multifractal modeling of long-range-dependent (LRD) traffic in computer communications networks. Nonlinear Analysis, 47(9), 5765–5774 (English summary). Proceedings of the Third world congress of nonlinear analysts, Part 9 (Catania, 2000) MathSciNetMATHCrossRef Gao, J., & Rubin, I. (2001). Multiplicative multifractal modeling of long-range-dependent (LRD) traffic in computer communications networks. Nonlinear Analysis, 47(9), 5765–5774 (English summary). Proceedings of the Third world congress of nonlinear analysts, Part 9 (Catania, 2000) MathSciNetMATHCrossRef
Zurück zum Zitat Georgii, H. O. (1988). Gibbs measure and phase transitions. Berlin: De Gruyter. CrossRef Georgii, H. O. (1988). Gibbs measure and phase transitions. Berlin: De Gruyter. CrossRef
Zurück zum Zitat Ghosh, S. (2009). The unseen species number revisited. Sankhya, The Indian Journal of Statistics, 71-B(2), 137–150. Ghosh, S. (2009). The unseen species number revisited. Sankhya, The Indian Journal of Statistics, 71-B(2), 137–150.
Zurück zum Zitat Giraitis, L., & Surgailis, D. (2002). ARCH-type bilinear models with double long memory. Stochastic Processes and Their Applications, 100, 275–300. MathSciNetMATHCrossRef Giraitis, L., & Surgailis, D. (2002). ARCH-type bilinear models with double long memory. Stochastic Processes and Their Applications, 100, 275–300. MathSciNetMATHCrossRef
Zurück zum Zitat Giraitis, L., Kokoska, P., & Leipus, R. (2000a). Stationary ARCH models: dependence structure and central limit theorem. Econometric Theory, 16, 3–22. MathSciNetMATHCrossRef Giraitis, L., Kokoska, P., & Leipus, R. (2000a). Stationary ARCH models: dependence structure and central limit theorem. Econometric Theory, 16, 3–22. MathSciNetMATHCrossRef
Zurück zum Zitat Giraitis, L., Kokoszka, P., Leipus, R., & Teyssière, G. (2000b). Semiparametric estimation of the intensity of long memory in conditional heteroskedasticity. Statistical Inference for Stochastic Processes, 3(1–2), 113–128. 19th “Rencontres Franco-Belges de statisticiens” (Marseille, 1998). MathSciNetMATHCrossRef Giraitis, L., Kokoszka, P., Leipus, R., & Teyssière, G. (2000b). Semiparametric estimation of the intensity of long memory in conditional heteroskedasticity. Statistical Inference for Stochastic Processes, 3(1–2), 113–128. 19th “Rencontres Franco-Belges de statisticiens” (Marseille, 1998). MathSciNetMATHCrossRef
Zurück zum Zitat Giraitis, L., Robinson, P. M., & Surgailis, D. (2000c). A model for long memory conditional heteroscedasticity. The Annals of Applied Probability, 10(3), 1002–1024. MathSciNetMATHCrossRef Giraitis, L., Robinson, P. M., & Surgailis, D. (2000c). A model for long memory conditional heteroscedasticity. The Annals of Applied Probability, 10(3), 1002–1024. MathSciNetMATHCrossRef
Zurück zum Zitat Giraitis, L., Kokoszka, P., Leipus, R., & Teyssiere, G. (2003). Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics, 112(2), 265–294. MathSciNetMATHCrossRef Giraitis, L., Kokoszka, P., Leipus, R., & Teyssiere, G. (2003). Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics, 112(2), 265–294. MathSciNetMATHCrossRef
Zurück zum Zitat Giraitis, L., Leipus, R., Robinson, P. M., & Surgailis, D. (2004). LARCH, leverage and long memory. Journal of Financial Econometrics, 2, 177–210. CrossRef Giraitis, L., Leipus, R., Robinson, P. M., & Surgailis, D. (2004). LARCH, leverage and long memory. Journal of Financial Econometrics, 2, 177–210. CrossRef
Zurück zum Zitat Giraitis, L., Leipus, R., & Surgailis, D. (2006). Recent advances in ARCH modelling. In G. Teyssière & A. P. Kirman (Eds.), Long memory in economics (pp. 3–38). Berlin: Springer. Giraitis, L., Leipus, R., & Surgailis, D. (2006). Recent advances in ARCH modelling. In G. Teyssière & A. P. Kirman (Eds.), Long memory in economics (pp. 3–38). Berlin: Springer.
Zurück zum Zitat Giraitis, L., Leipus, R., & Surgailis, D. (2010). Aggregation of the random coefficient GLARCH(1, 1) process. Econometric Theory, 26, 406–425. MathSciNetMATHCrossRef Giraitis, L., Leipus, R., & Surgailis, D. (2010). Aggregation of the random coefficient GLARCH(1, 1) process. Econometric Theory, 26, 406–425. MathSciNetMATHCrossRef
Zurück zum Zitat Goncalves, E., & Gouriéroux, C. (1988). Aggrégation de processus autoregressifs d’ordre 1. Annales d’Économie et de Statistique, 12, 127–149. Goncalves, E., & Gouriéroux, C. (1988). Aggrégation de processus autoregressifs d’ordre 1. Annales d’Économie et de Statistique, 12, 127–149.
Zurück zum Zitat Gorostiza, L. G., & Wakolbinger, A. (1991). Persistence criteria for a class of critical branching particle systems in continuous time. Annals of Probability, 19, 266–288. MathSciNetMATHCrossRef Gorostiza, L. G., & Wakolbinger, A. (1991). Persistence criteria for a class of critical branching particle systems in continuous time. Annals of Probability, 19, 266–288. MathSciNetMATHCrossRef
Zurück zum Zitat Gorostiza, L. G., Navarro, R., & Rodrigues, E. R. (2005). Some long-range dependence processes arising from fluctuations of particle systems. Acta Applicandae Mathematicae, 86, 285–308. MathSciNetMATHCrossRef Gorostiza, L. G., Navarro, R., & Rodrigues, E. R. (2005). Some long-range dependence processes arising from fluctuations of particle systems. Acta Applicandae Mathematicae, 86, 285–308. MathSciNetMATHCrossRef
Zurück zum Zitat Gouyet, J.-F. (1996). Physics and fractal structures. New York: Springer. Gouyet, J.-F. (1996). Physics and fractal structures. New York: Springer.
Zurück zum Zitat Gradshteyn, I. S., & Rhyzhik, I. M. (1965). Tables of integrals, series and products. San Diego: Academic Press. Gradshteyn, I. S., & Rhyzhik, I. M. (1965). Tables of integrals, series and products. San Diego: Academic Press.
Zurück zum Zitat Granger, C. W. J. (1966). The typical spectral shape of an economic variable. Econometrica, 34, 150–161. CrossRef Granger, C. W. J. (1966). The typical spectral shape of an economic variable. Econometrica, 34, 150–161. CrossRef
Zurück zum Zitat Granger, C. (1980). Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, 14, 227–238. MathSciNetMATHCrossRef Granger, C. (1980). Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, 14, 227–238. MathSciNetMATHCrossRef
Zurück zum Zitat Granger, C. W. J. (1998). Real and spurious long-memory properties of stock market data: comment. Journal of Business and Economic Statistics, 16, 268–269. Granger, C. W. J. (1998). Real and spurious long-memory properties of stock market data: comment. Journal of Business and Economic Statistics, 16, 268–269.
Zurück zum Zitat Granger, C. W. J., & Hyung, N. (2004). Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. Journal of Empirical Finance, 11, 399–421. CrossRef Granger, C. W. J., & Hyung, N. (2004). Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. Journal of Empirical Finance, 11, 399–421. CrossRef
Zurück zum Zitat Granger, C. W. J., & Joyeux, R. (1980). An introduction to long-range time series models and fractional differencing. Journal of Time Series Analysis, 1, 15–30. MathSciNetMATHCrossRef Granger, C. W. J., & Joyeux, R. (1980). An introduction to long-range time series models and fractional differencing. Journal of Time Series Analysis, 1, 15–30. MathSciNetMATHCrossRef
Zurück zum Zitat Greiner, M., Jobmann, M., & Klüppelberg, C. (1999). Telecommunication traffic, queueing models, and subexponential distributions. Queues with heavy-tailed distributions. Queueing Systems, Theory and Applications, 33(1–3), 125–152. MathSciNetMATHCrossRef Greiner, M., Jobmann, M., & Klüppelberg, C. (1999). Telecommunication traffic, queueing models, and subexponential distributions. Queues with heavy-tailed distributions. Queueing Systems, Theory and Applications, 33(1–3), 125–152. MathSciNetMATHCrossRef
Zurück zum Zitat Grimmett, G. (1999). Percolation (2nd ed.). Berlin: Springer. MATH Grimmett, G. (1999). Percolation (2nd ed.). Berlin: Springer. MATH
Zurück zum Zitat Guasoni, P. (2006). No arbitrage under transaction costs, with fractional Brownian motion and beyond. Mathematical Finance, 16, 569–582. MathSciNetMATHCrossRef Guasoni, P. (2006). No arbitrage under transaction costs, with fractional Brownian motion and beyond. Mathematical Finance, 16, 569–582. MathSciNetMATHCrossRef
Zurück zum Zitat Harte, J., Kinzig, A., & Green, J. (1999). Self-similarity in the distribution and abundance of species. Science, 284, 334–336. CrossRef Harte, J., Kinzig, A., & Green, J. (1999). Self-similarity in the distribution and abundance of species. Science, 284, 334–336. CrossRef
Zurück zum Zitat Harvey, A. (1998). Long memory in stochastic volatility. In J. Knight & S. Satchell (Eds.), Forecasting volatility in the financial markets (pp. 307–320). Oxford: Butterworth-Heineman. Harvey, A. (1998). Long memory in stochastic volatility. In J. Knight & S. Satchell (Eds.), Forecasting volatility in the financial markets (pp. 307–320). Oxford: Butterworth-Heineman.
Zurück zum Zitat Harvey, A. C. (2007). Long memory in stochastic volatility. In J. Knight & S. Satchell (Eds.), Forecasting volatility in the financial markets (3rd ed., pp. 351–363). Oxford: Butterworth-Heineman. CrossRef Harvey, A. C. (2007). Long memory in stochastic volatility. In J. Knight & S. Satchell (Eds.), Forecasting volatility in the financial markets (3rd ed., pp. 351–363). Oxford: Butterworth-Heineman. CrossRef
Zurück zum Zitat Hassler, U. (2011). Estimation of fractional integration under temporal aggregation. Journal of Econometrics, 162(2), 240–247. MathSciNetCrossRef Hassler, U. (2011). Estimation of fractional integration under temporal aggregation. Journal of Econometrics, 162(2), 240–247. MathSciNetCrossRef
Zurück zum Zitat Heath, D., Resnick, S., & Samorodnitsky, G. (1998). Heavy tails and long range dependence in on/off processes and associated circuit models. Mathematics of Operations Research, 23, 145–165. MathSciNetMATHCrossRef Heath, D., Resnick, S., & Samorodnitsky, G. (1998). Heavy tails and long range dependence in on/off processes and associated circuit models. Mathematics of Operations Research, 23, 145–165. MathSciNetMATHCrossRef
Zurück zum Zitat Heck, A. & Pedang, J. M. (Eds.) (1991). Applying fractals in astronomy. Berlin: Springer. Heck, A. & Pedang, J. M. (Eds.) (1991). Applying fractals in astronomy. Berlin: Springer.
Zurück zum Zitat Henry, M., & Zaffaroni, P. (2003). The long range dependence paradigm for macroeconomics and finance. In P. Doukhan, G. Oppenheim, & M. Taqqu (Eds.), The theory and applications of long-range dependence, Boston: Birkhäuser. Henry, M., & Zaffaroni, P. (2003). The long range dependence paradigm for macroeconomics and finance. In P. Doukhan, G. Oppenheim, & M. Taqqu (Eds.), The theory and applications of long-range dependence, Boston: Birkhäuser.
Zurück zum Zitat Hernandez-Campos, F., Marron, J. S., Samorodnitsky, G., & Smith, F. D. (2002). Variable heavy tailed durations in Internet traffic: part I, understanding heavy tails. In Proc. of the 10th IEEE intl. sympos. on modeling, analysis and simulation of computer and telecommunications systems (MASCOTS 2002), IEEE (pp. 43–50). CrossRef Hernandez-Campos, F., Marron, J. S., Samorodnitsky, G., & Smith, F. D. (2002). Variable heavy tailed durations in Internet traffic: part I, understanding heavy tails. In Proc. of the 10th IEEE intl. sympos. on modeling, analysis and simulation of computer and telecommunications systems (MASCOTS 2002), IEEE (pp. 43–50). CrossRef
Zurück zum Zitat Hsieh, M.-C., Hurvich, C. M., & Soulier, P. (2007). Asymptotics for duration-driven long range dependent processes. Journal of Econometrics, 141(2), 913–949. MathSciNetCrossRef Hsieh, M.-C., Hurvich, C. M., & Soulier, P. (2007). Asymptotics for duration-driven long range dependent processes. Journal of Econometrics, 141(2), 913–949. MathSciNetCrossRef
Zurück zum Zitat Hu, Y. (2005). Integral transformations and anticipative calculus for fractional Brownian motions. Memoirs of the American Mathematical Society, 175, 825. CrossRef Hu, Y. (2005). Integral transformations and anticipative calculus for fractional Brownian motions. Memoirs of the American Mathematical Society, 175, 825. CrossRef
Zurück zum Zitat Hu, Y., & Nualart, D. (2010). Parameter estimation for fractional Ornstein–Uhlenbeck processes. Statistics & Probability Letters, 80(11–12), 1030–1038. MathSciNetMATHCrossRef Hu, Y., & Nualart, D. (2010). Parameter estimation for fractional Ornstein–Uhlenbeck processes. Statistics & Probability Letters, 80(11–12), 1030–1038. MathSciNetMATHCrossRef
Zurück zum Zitat Hu, Y., & Øksendal, B. (2003). Fractional white noise calculus and applications to finance. Infinite Dimensional Analysis, Quantum Probability, and Related Topics, 6, 1–32. MATHCrossRef Hu, Y., & Øksendal, B. (2003). Fractional white noise calculus and applications to finance. Infinite Dimensional Analysis, Quantum Probability, and Related Topics, 6, 1–32. MATHCrossRef
Zurück zum Zitat Hwang, S. (2000). The effects of systematic sampling and temporal aggregation on discrete time long memory processes and their finite sample properties. Econometric Theory, 16, 347–372. MathSciNetMATHCrossRef Hwang, S. (2000). The effects of systematic sampling and temporal aggregation on discrete time long memory processes and their finite sample properties. Econometric Theory, 16, 347–372. MathSciNetMATHCrossRef
Zurück zum Zitat Igloi, E., & Terdik, G. (1999). Long-range dependence through gamma-mixed Ornstein–Uhlenbeck process. Electronic Journal of Probability, 4(16), 1–33. MathSciNet Igloi, E., & Terdik, G. (1999). Long-range dependence through gamma-mixed Ornstein–Uhlenbeck process. Electronic Journal of Probability, 4(16), 1–33. MathSciNet
Zurück zum Zitat Imbrie, J., & Newman, C. (1988). An intermediate phase with slow decay of correlations in one dimensional 1/|x−y|2 percolation, Ising and Potts models. Communications in Mathematical Physics, 118, 303–336. MathSciNetCrossRef Imbrie, J., & Newman, C. (1988). An intermediate phase with slow decay of correlations in one dimensional 1/|xy|2 percolation, Ising and Potts models. Communications in Mathematical Physics, 118, 303–336. MathSciNetCrossRef
Zurück zum Zitat Járai, A. A. (2003). Invasion percolation and the incipient infinite cluster in 2D. Journal of Communications in Mathematical Physics, 236(2), 311–334. MATHCrossRef Járai, A. A. (2003). Invasion percolation and the incipient infinite cluster in 2D. Journal of Communications in Mathematical Physics, 236(2), 311–334. MATHCrossRef
Zurück zum Zitat Jasiak, J. (1998). Persistence in intratrade durations. Finance, 19, 166–195. Jasiak, J. (1998). Persistence in intratrade durations. Finance, 19, 166–195.
Zurück zum Zitat Jelenkovič, P. R., & Lazar, A. A. (1999). Asymptotic results for multiplexing subexponential on–off processes. Advances in Applied Probability, 31(2), 394–421. MathSciNetMATHCrossRef Jelenkovič, P. R., & Lazar, A. A. (1999). Asymptotic results for multiplexing subexponential on–off processes. Advances in Applied Probability, 31(2), 394–421. MathSciNetMATHCrossRef
Zurück zum Zitat Kaj, I. (2002). Stochastic modeling in broadband communications systems. SIAM monographs on mathematical modeling and computation. Philadelphia: Society for Industrial and Applied Mathematics (SIAM). xvi+177 pp. MATHCrossRef Kaj, I. (2002). Stochastic modeling in broadband communications systems. SIAM monographs on mathematical modeling and computation. Philadelphia: Society for Industrial and Applied Mathematics (SIAM). xvi+177 pp. MATHCrossRef
Zurück zum Zitat Kasahara, Y., Maejima, M., & Vervaat, W. (1988). Logfractional stable processes. Stochastic Processes and Their Applications, 30, 329–339. MathSciNetMATHCrossRef Kasahara, Y., Maejima, M., & Vervaat, W. (1988). Logfractional stable processes. Stochastic Processes and Their Applications, 30, 329–339. MathSciNetMATHCrossRef
Zurück zum Zitat Kaufman, B., & Onsager, L. (1949). Crystal statistics III: short-range order in a binary Ising lattice. Physical Review, 76, 1244–1252. MATHCrossRef Kaufman, B., & Onsager, L. (1949). Crystal statistics III: short-range order in a binary Ising lattice. Physical Review, 76, 1244–1252. MATHCrossRef
Zurück zum Zitat Kazakevičius, V., & Leipus, R. (2003). A new theorem on the existence of invariant distributions with applications to ARCH processes. Journal of Applied Probability, 40(1), 147–162. MathSciNetMATHCrossRef Kazakevičius, V., & Leipus, R. (2003). A new theorem on the existence of invariant distributions with applications to ARCH processes. Journal of Applied Probability, 40(1), 147–162. MathSciNetMATHCrossRef
Zurück zum Zitat Kazakevičius, V., Leipus, R., & Viano, M.-C. (2004). Stability of random coefficient ARCH models and aggregation schemes. Journal of Econometrics, 120(1), 139–158. MathSciNetCrossRef Kazakevičius, V., Leipus, R., & Viano, M.-C. (2004). Stability of random coefficient ARCH models and aggregation schemes. Journal of Econometrics, 120(1), 139–158. MathSciNetCrossRef
Zurück zum Zitat Kesten, H. (1982). Progress in probability and statistics: Vol. 2. Percolation theory for mathematicians. Boston: Birkhäuser. MATH Kesten, H. (1982). Progress in probability and statistics: Vol. 2. Percolation theory for mathematicians. Boston: Birkhäuser. MATH
Zurück zum Zitat Kirman, A., & Teyssière, G. (2002). Microeconomic models for long memory in the volatility of financial time series. Studies in Nonlinear Dynamics & Econometrics, 5(4), 40–61. CrossRef Kirman, A., & Teyssière, G. (2002). Microeconomic models for long memory in the volatility of financial time series. Studies in Nonlinear Dynamics & Econometrics, 5(4), 40–61. CrossRef
Zurück zum Zitat Kleptsyna, M. L., & Le Breton, A. (2002). Statistical analysis of the fractional Ornstein–Uhlenbeck type process. Statistical Inference for Stochastic Processes, 5, 229–248. MathSciNetMATHCrossRef Kleptsyna, M. L., & Le Breton, A. (2002). Statistical analysis of the fractional Ornstein–Uhlenbeck type process. Statistical Inference for Stochastic Processes, 5, 229–248. MathSciNetMATHCrossRef
Zurück zum Zitat Kleptsyna, M. L., Le Breton, A., & Roubaud, M.-C. (2000). Parameter estimation and optimal filtering for fractional type stochastic systems. Statistical Inference for Stochastic Processes, 3, 173–182. MathSciNetMATHCrossRef Kleptsyna, M. L., Le Breton, A., & Roubaud, M.-C. (2000). Parameter estimation and optimal filtering for fractional type stochastic systems. Statistical Inference for Stochastic Processes, 3, 173–182. MathSciNetMATHCrossRef
Zurück zum Zitat Klüppelberg, C., & Kühn, C. (2004). Fractional Brownian motion as a weak limit of Poisson shot noise processes—with applications to finance. Stochastic Processes and Their Applications, 113(2), 333–351. MathSciNetMATHCrossRef Klüppelberg, C., & Kühn, C. (2004). Fractional Brownian motion as a weak limit of Poisson shot noise processes—with applications to finance. Stochastic Processes and Their Applications, 113(2), 333–351. MathSciNetMATHCrossRef
Zurück zum Zitat Klüppelberg, C., Mikosch, T., & Schärf, A. (2003). Regular variation in the mean and stable limits for Poisson shot noise. Bernoulli, 9(3), 467–496 (English summary). MathSciNetMATHCrossRef Klüppelberg, C., Mikosch, T., & Schärf, A. (2003). Regular variation in the mean and stable limits for Poisson shot noise. Bernoulli, 9(3), 467–496 (English summary). MathSciNetMATHCrossRef
Zurück zum Zitat Kokoszka, P. S. (1996). Prediction of infinite variance fractional ARIMA. Probability and Mathematical Statistics, 16, 65–83. MathSciNetMATH Kokoszka, P. S. (1996). Prediction of infinite variance fractional ARIMA. Probability and Mathematical Statistics, 16, 65–83. MathSciNetMATH
Zurück zum Zitat Kokoszka, P. S., & Mikosch, T. (1997). The integrated periodogram for long-memory processes with finite or infinite variance. Stochastic Processes and Their Applications, 66(1), 55–78. MathSciNetMATHCrossRef Kokoszka, P. S., & Mikosch, T. (1997). The integrated periodogram for long-memory processes with finite or infinite variance. Stochastic Processes and Their Applications, 66(1), 55–78. MathSciNetMATHCrossRef
Zurück zum Zitat Kokoszka, P. S., & Taqqu, M. S. (1993). Asymptotic dependence of moving average type self-similar stable random fields. Nagoya Mathematical Journal, 130, 85–100. MathSciNetMATH Kokoszka, P. S., & Taqqu, M. S. (1993). Asymptotic dependence of moving average type self-similar stable random fields. Nagoya Mathematical Journal, 130, 85–100. MathSciNetMATH
Zurück zum Zitat Kokoszka, P. S., & Taqqu, M. S. (1995a). Fractional ARIMA with stable innovations. Stochastic Processes and Their Applications, 60, 19–47. MathSciNetMATHCrossRef Kokoszka, P. S., & Taqqu, M. S. (1995a). Fractional ARIMA with stable innovations. Stochastic Processes and Their Applications, 60, 19–47. MathSciNetMATHCrossRef
Zurück zum Zitat Kokoszka, P. S., & Taqqu, M. S. (1995b). Infinite variance stable moving averages with long memory. Journal of Econometrics, 73, 79–99. MathSciNetCrossRef Kokoszka, P. S., & Taqqu, M. S. (1995b). Infinite variance stable moving averages with long memory. Journal of Econometrics, 73, 79–99. MathSciNetCrossRef
Zurück zum Zitat Kokoszka, P. S., & Taqqu, M. S. (1996). Parameter estimation for infinite variance fractional ARIMA. The Annals of Statistics, 24(5), 1880–1913. MathSciNetMATHCrossRef Kokoszka, P. S., & Taqqu, M. S. (1996). Parameter estimation for infinite variance fractional ARIMA. The Annals of Statistics, 24(5), 1880–1913. MathSciNetMATHCrossRef
Zurück zum Zitat Kokoszka, P. S., & Taqqu, M. S. (2001). Can one use the Durbin–Levinson algorithm to generate infinite variance fractional ARIMA time series? Journal of Time Series Analysis, 22, 317–337. MathSciNetMATHCrossRef Kokoszka, P. S., & Taqqu, M. S. (2001). Can one use the Durbin–Levinson algorithm to generate infinite variance fractional ARIMA time series? Journal of Time Series Analysis, 22, 317–337. MathSciNetMATHCrossRef
Zurück zum Zitat Kolmogorov, A. N. (1940). Wienersche Spiralen und einige andere interessante Kurven in Hilbertschen Raum. Comptes Rendus (Doklady) Academy of Sciences of the USSR (N.S.), 26, 115–118. Kolmogorov, A. N. (1940). Wienersche Spiralen und einige andere interessante Kurven in Hilbertschen Raum. Comptes Rendus (Doklady) Academy of Sciences of the USSR (N.S.), 26, 115–118.
Zurück zum Zitat Kolmogorov, A. N. (1941). Local structure of turbulence in fluid for very large Reynolds numbers. In S. K. Friedlander & L. Topper (Eds.), Transl. in turbulence (pp. 151–155). New York: Interscience. 1961. Kolmogorov, A. N. (1941). Local structure of turbulence in fluid for very large Reynolds numbers. In S. K. Friedlander & L. Topper (Eds.), Transl. in turbulence (pp. 151–155). New York: Interscience. 1961.
Zurück zum Zitat Konstantopoulos, T., & Lin, S.-J. (1998). Macroscopic models for long-range dependent network traffic. Queueing Systems, Theory and Applications, 28(1–3), 215–243. MathSciNetMATHCrossRef Konstantopoulos, T., & Lin, S.-J. (1998). Macroscopic models for long-range dependent network traffic. Queueing Systems, Theory and Applications, 28(1–3), 215–243. MathSciNetMATHCrossRef
Zurück zum Zitat Kosterlitz, J. M., & Thouless, D. J. (1978). Progress in low temperature physics: Vol. VIIB. Two-dimensional physics (p. 371). Amsterdam: North-Holland. Kosterlitz, J. M., & Thouless, D. J. (1978). Progress in low temperature physics: Vol. VIIB. Two-dimensional physics (p. 371). Amsterdam: North-Holland.
Zurück zum Zitat Koul, H. L., & Surgailis, D. (2001). Asymptotics of empirical processes of long memory moving averages with infinite variance. Stochastic Processes and Their Applications, 91(2), 309–336. MathSciNetMATHCrossRef Koul, H. L., & Surgailis, D. (2001). Asymptotics of empirical processes of long memory moving averages with infinite variance. Stochastic Processes and Their Applications, 91(2), 309–336. MathSciNetMATHCrossRef
Zurück zum Zitat Kulik, R., & Soulier, P. (2011). The tail empirical process for long memory stochastic volatility sequences. Stochastic Processes and Their Applications, 121(1), 109–134. MathSciNetMATHCrossRef Kulik, R., & Soulier, P. (2011). The tail empirical process for long memory stochastic volatility sequences. Stochastic Processes and Their Applications, 121(1), 109–134. MathSciNetMATHCrossRef
Zurück zum Zitat Kulik, R., & Soulier, P. (2012). Limit theorems for long memory stochastic volatility models with infinite variance: partial sums and sample covariances. Advances in Applied Probability, 44(4), 1113–1141. MATHCrossRef Kulik, R., & Soulier, P. (2012). Limit theorems for long memory stochastic volatility models with infinite variance: partial sums and sample covariances. Advances in Applied Probability, 44(4), 1113–1141. MATHCrossRef
Zurück zum Zitat Kulik, R., & Soulier, P. (2013, in press). Estimation of limiting conditional distributions for the heavy tailed long memory stochastic volatility process. Extremes. Kulik, R., & Soulier, P. (2013, in press). Estimation of limiting conditional distributions for the heavy tailed long memory stochastic volatility process. Extremes.
Zurück zum Zitat Kulik, R., & Szekli, R. (2001). Sufficient conditions for long range count dependence of stationary point processes on the real line. Journal of Applied Probability, 38, 570–581. MathSciNetMATHCrossRef Kulik, R., & Szekli, R. (2001). Sufficient conditions for long range count dependence of stationary point processes on the real line. Journal of Applied Probability, 38, 570–581. MathSciNetMATHCrossRef
Zurück zum Zitat Künsch, H. (1980). Reellwertige Zufallsfelder auf einem Gitter: Interpolationsprobleme, Variationsprinzip und statistische Analyse. Ph.D. thesis, ETH Zurich. Künsch, H. (1980). Reellwertige Zufallsfelder auf einem Gitter: Interpolationsprobleme, Variationsprinzip und statistische Analyse. Ph.D. thesis, ETH Zurich.
Zurück zum Zitat Lamperti, J. W. (1972). Semi-stable Markov processes. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 22, 205–225. MathSciNetMATHCrossRef Lamperti, J. W. (1972). Semi-stable Markov processes. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 22, 205–225. MathSciNetMATHCrossRef
Zurück zum Zitat Lanford, O. E., & Ruelle, D. (1968). Observables at infinity and states with short-range correlations in statistical mechanics. Communications in Mathematical Physics, 13(3), 194–215. MathSciNetCrossRef Lanford, O. E., & Ruelle, D. (1968). Observables at infinity and states with short-range correlations in statistical mechanics. Communications in Mathematical Physics, 13(3), 194–215. MathSciNetCrossRef
Zurück zum Zitat Lanford, O. E., & Ruelle, D. (1969). Observables at infinity and states with short range correlations in statistical mechanics. Communications in Mathematical Physics, 13, 194–215. MathSciNetCrossRef Lanford, O. E., & Ruelle, D. (1969). Observables at infinity and states with short range correlations in statistical mechanics. Communications in Mathematical Physics, 13, 194–215. MathSciNetCrossRef
Zurück zum Zitat Lavancier, F. (2006). Long memory random fields. In P. Doukhan, P. Bertail, & P. Soulier (Eds.), Lecture notes in statistics: Vol. 187. Dependence in probability and statistics (pp. 195–220). New York: Springer. CrossRef Lavancier, F. (2006). Long memory random fields. In P. Doukhan, P. Bertail, & P. Soulier (Eds.), Lecture notes in statistics: Vol. 187. Dependence in probability and statistics (pp. 195–220). New York: Springer. CrossRef
Zurück zum Zitat Le Breton, A. (1998). Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion. Statistics & Probability Letters, 38(3), 263–274. MathSciNetMATHCrossRef Le Breton, A. (1998). Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion. Statistics & Probability Letters, 38(3), 263–274. MathSciNetMATHCrossRef
Zurück zum Zitat Leipus, R., & Surgailis, D. (2007). On long-range dependence in regenerative processes based on a general ON/OFF scheme. Journal of Applied Probability, 44(2), 379–392. MathSciNetMATHCrossRef Leipus, R., & Surgailis, D. (2007). On long-range dependence in regenerative processes based on a general ON/OFF scheme. Journal of Applied Probability, 44(2), 379–392. MathSciNetMATHCrossRef
Zurück zum Zitat Leipus, R., & Viano, M.-C. (2002). Aggregation in ARCH models. Lithuanian Mathematical Journal, 42, 68–89. MathSciNetCrossRef Leipus, R., & Viano, M.-C. (2002). Aggregation in ARCH models. Lithuanian Mathematical Journal, 42, 68–89. MathSciNetCrossRef
Zurück zum Zitat Leipus, R., Oppenheim, G., Philippe, A., & Viano, M.-C. (2006). Orthogonal series density estimation in a disaggregation scheme. Journal of Statistical Planning and Inference, 136(8), 2547–2571. MathSciNetMATHCrossRef Leipus, R., Oppenheim, G., Philippe, A., & Viano, M.-C. (2006). Orthogonal series density estimation in a disaggregation scheme. Journal of Statistical Planning and Inference, 136(8), 2547–2571. MathSciNetMATHCrossRef
Zurück zum Zitat Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1993a). Statistical analysis of high-time resolution Ethernet LAN traffic measurements. In M. E. Tarter & M. D. Lock (Eds.), Computing science and statistics: Vol. 25. Statistical applications of expanding computer capabilities. Proceedings of the 25th symposium on the interface between statistics and computer science (pp. 146–155). Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1993a). Statistical analysis of high-time resolution Ethernet LAN traffic measurements. In M. E. Tarter & M. D. Lock (Eds.), Computing science and statistics: Vol. 25. Statistical applications of expanding computer capabilities. Proceedings of the 25th symposium on the interface between statistics and computer science (pp. 146–155).
Zurück zum Zitat Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1993b). On the self-similar nature of ethernet traffic. In Proc. ACM SIGCOMM 1993, San Francisco, CA (pp. 183–193). Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1993b). On the self-similar nature of ethernet traffic. In Proc. ACM SIGCOMM 1993, San Francisco, CA (pp. 183–193).
Zurück zum Zitat Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1994). On the self-similar nature (extended version). IEEE/ACM Transactions on Networking, 2(1), 1–15. CrossRef Leland, W. E., Taqqu, M. S., Willinger, W., & Wilson, D. V. (1994). On the self-similar nature (extended version). IEEE/ACM Transactions on Networking, 2(1), 1–15. CrossRef
Zurück zum Zitat Leonenko, N., & Ruiz-Medina, M. (2006). Scaling laws for the multidimensional Burgers equation with quadratic external potential. Journal of Statistical Physics, 124(1), 191–205. MathSciNetMATHCrossRef Leonenko, N., & Ruiz-Medina, M. (2006). Scaling laws for the multidimensional Burgers equation with quadratic external potential. Journal of Statistical Physics, 124(1), 191–205. MathSciNetMATHCrossRef
Zurück zum Zitat Leonenko, N., & Taufer, E. (2005). Convergence of integrated superpositions of Ornstein–Uhlenbeck processes to fractional Brownian motion. Stochastics: An International Journal of Probability and Stochastic Processes, 77(6), 477–499. MathSciNetMATHCrossRef Leonenko, N., & Taufer, E. (2005). Convergence of integrated superpositions of Ornstein–Uhlenbeck processes to fractional Brownian motion. Stochastics: An International Journal of Probability and Stochastic Processes, 77(6), 477–499. MathSciNetMATHCrossRef
Zurück zum Zitat Levy, J. B., & Taqqu, M. S. (1986). Using renewal processes to generate long-range dependence and high variability. In Progr. probab. statist.: Vol. 11. Dependence in probability and statistics, Oberwolfach, 1985 (pp. 73–89). Boston: Birkhäuser Boston. Levy, J. B., & Taqqu, M. S. (1986). Using renewal processes to generate long-range dependence and high variability. In Progr. probab. statist.: Vol. 11. Dependence in probability and statistics, Oberwolfach, 1985 (pp. 73–89). Boston: Birkhäuser Boston.
Zurück zum Zitat Levy, J. B., & Taqqu, M. S. (1987). On renewal processes having stable inter-renewal intervals and stable rewards. Annales Des Sciences Mathématiques Du Québec, 11(1), 95–110. MathSciNetMATH Levy, J. B., & Taqqu, M. S. (1987). On renewal processes having stable inter-renewal intervals and stable rewards. Annales Des Sciences Mathématiques Du Québec, 11(1), 95–110. MathSciNetMATH
Zurück zum Zitat Levy, J. B., & Taqqu, M. S. (2000). Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. Bernoulli, 6(1), 23–44. MathSciNetMATHCrossRef Levy, J. B., & Taqqu, M. S. (2000). Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. Bernoulli, 6(1), 23–44. MathSciNetMATHCrossRef
Zurück zum Zitat Levy, J. B., & Taqqu, M. S. (2001). Dependence structure of a renewal-reward process with infinite variance. Fractals, 9(2), 185–192. MathSciNetMATHCrossRef Levy, J. B., & Taqqu, M. S. (2001). Dependence structure of a renewal-reward process with infinite variance. Fractals, 9(2), 185–192. MathSciNetMATHCrossRef
Zurück zum Zitat Levy, J. B., & Taqqu, M. S. (2005). The asymptotic codifference and covariation of log fractional stable noise. Preprint. Levy, J. B., & Taqqu, M. S. (2005). The asymptotic codifference and covariation of log fractional stable noise. Preprint.
Zurück zum Zitat Liggett, T. M. (2004). Interacting particle systems. Classics in mathematics. Berlin: Springer. Liggett, T. M. (2004). Interacting particle systems. Classics in mathematics. Berlin: Springer.
Zurück zum Zitat Ling, S., & Li, W. K. (1997). On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. Journal of the American Statistical Association, 92, 1184–1194. MathSciNetMATHCrossRef Ling, S., & Li, W. K. (1997). On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. Journal of the American Statistical Association, 92, 1184–1194. MathSciNetMATHCrossRef
Zurück zum Zitat Lobato, I. N., & Savin, N. E. (1998). Real and spurious long-memory properties of stock-market data. Journal of Business & Economic Statistics, 16(3), 261–268. MathSciNet Lobato, I. N., & Savin, N. E. (1998). Real and spurious long-memory properties of stock-market data. Journal of Business & Economic Statistics, 16(3), 261–268. MathSciNet
Zurück zum Zitat Lowen, S. B., & Teich, M. C. (2005). Fractal based point processes. New York: Wiley. MATHCrossRef Lowen, S. B., & Teich, M. C. (2005). Fractal based point processes. New York: Wiley. MATHCrossRef
Zurück zum Zitat Maejima, M., & Yamamoto, K. (2003). Long-memory stable Ornstein–Uhlenbeck processes. Electronic Journal of Probability, 8(19), 1–18. MathSciNet Maejima, M., & Yamamoto, K. (2003). Long-memory stable Ornstein–Uhlenbeck processes. Electronic Journal of Probability, 8(19), 1–18. MathSciNet
Zurück zum Zitat Man, K. S., & Tiao, G. C. (2006). Aggregation effect and forecasting temporal aggregates of long memory processes. International Journal of Forecasting, 22(2), 267–281. CrossRef Man, K. S., & Tiao, G. C. (2006). Aggregation effect and forecasting temporal aggregates of long memory processes. International Journal of Forecasting, 22(2), 267–281. CrossRef
Zurück zum Zitat Man, K. S., & Tiao, G. C. (2009). ARFIMA approximation and forecasting of the limiting aggregate structure of long-memory process. Journal of Forecasting, 28, 89–101. MathSciNetCrossRef Man, K. S., & Tiao, G. C. (2009). ARFIMA approximation and forecasting of the limiting aggregate structure of long-memory process. Journal of Forecasting, 28, 89–101. MathSciNetCrossRef
Zurück zum Zitat Mandelbrot, B. B. (1971). When can price be arbitraged efficiently? A limit to the validity of the random walk and martingale models. Reviews of Economics and Statistics, LIII, 225–236. MathSciNetCrossRef Mandelbrot, B. B. (1971). When can price be arbitraged efficiently? A limit to the validity of the random walk and martingale models. Reviews of Economics and Statistics, LIII, 225–236. MathSciNetCrossRef
Zurück zum Zitat Mandelbrot, B. B. (1977). Fractals: form, chance and dimension. San Francisco: Freeman. MATH Mandelbrot, B. B. (1977). Fractals: form, chance and dimension. San Francisco: Freeman. MATH
Zurück zum Zitat Mandelbrot, B. B. (1983). The fractal geometry of nature. San Francisco: Freeman. Mandelbrot, B. B. (1983). The fractal geometry of nature. San Francisco: Freeman.
Zurück zum Zitat Mandelbrot, B. B. (1997). Fractals and scaling in finance: discontinuity, concentration, risk. New York: Springer. MATHCrossRef Mandelbrot, B. B. (1997). Fractals and scaling in finance: discontinuity, concentration, risk. New York: Springer. MATHCrossRef
Zurück zum Zitat Mandelbrot, B. B. (1999). Multifractals and 1/f noise: wild self-affinity in physics. New York: Springer. Mandelbrot, B. B. (1999). Multifractals and 1/f noise: wild self-affinity in physics. New York: Springer.
Zurück zum Zitat Mandelbrot, B. B. (2002). Gaussian self-affinity and fractals. Globality, the earth, 2/f noise, and R/S. New York: Springer. Mandelbrot, B. B. (2002). Gaussian self-affinity and fractals. Globality, the earth, 2/f noise, and R/S. New York: Springer.
Zurück zum Zitat Mansfield, P., Rachev, S., & Samorodnitsky, G. (2001). Long strange segments of a stochastic process and long range dependence. The Annals of Applied Probability, 11, 878–921. MathSciNetMATHCrossRef Mansfield, P., Rachev, S., & Samorodnitsky, G. (2001). Long strange segments of a stochastic process and long range dependence. The Annals of Applied Probability, 11, 878–921. MathSciNetMATHCrossRef
Zurück zum Zitat Marinari, E., Parisi, G., Ruelle, D., & Widney, P. (1983). On the interpretation of 1/f noise. Communications in Mathematical Physics, 89, 1–12. MathSciNetMATHCrossRef Marinari, E., Parisi, G., Ruelle, D., & Widney, P. (1983). On the interpretation of 1/f noise. Communications in Mathematical Physics, 89, 1–12. MathSciNetMATHCrossRef
Zurück zum Zitat Matsui, M., & Shieh, N.-R. (2009). On the exponentials of fractional Ornstein–Uhlenbeck processes. Electronic Journal of Probability, 14(23), 594–611. MathSciNetMATH Matsui, M., & Shieh, N.-R. (2009). On the exponentials of fractional Ornstein–Uhlenbeck processes. Electronic Journal of Probability, 14(23), 594–611. MathSciNetMATH
Zurück zum Zitat Maulik, K., Resnick, S., & Rootzen, H. (2002). Asymptotic independence and a network traffic model. Journal of Applied Probability, 39(4), 671–699. MathSciNetMATHCrossRef Maulik, K., Resnick, S., & Rootzen, H. (2002). Asymptotic independence and a network traffic model. Journal of Applied Probability, 39(4), 671–699. MathSciNetMATHCrossRef
Zurück zum Zitat McCauley, J. L. (1993). Chaos, dynamics and fractals. Cambridge: Cambridge University Press. MATH McCauley, J. L. (1993). Chaos, dynamics and fractals. Cambridge: Cambridge University Press. MATH
Zurück zum Zitat McMullen, C. T. (1994). Complex dynamics and renormalization. Princeton: Princeton University Press. McMullen, C. T. (1994). Complex dynamics and renormalization. Princeton: Princeton University Press.
Zurück zum Zitat Meakin, P. (1998). Fractals, scaling and growth far from equilibrium. Cambridge: Cambridge University Press. MATH Meakin, P. (1998). Fractals, scaling and growth far from equilibrium. Cambridge: Cambridge University Press. MATH
Zurück zum Zitat Meester, R., & Steif, J. E. (1996). On the continuity of the critical value for long-range percolation in the exponential case. Communications in Mathematical Physics, 180, 483–504. MathSciNetMATHCrossRef Meester, R., & Steif, J. E. (1996). On the continuity of the critical value for long-range percolation in the exponential case. Communications in Mathematical Physics, 180, 483–504. MathSciNetMATHCrossRef
Zurück zum Zitat Menshikov, M., Sidoravicius, V., & Vachkovskaia, M. (2001). A note on two-dimensional truncated long-range percolation. Advances in Applied Probability, 33, 912–929. MathSciNetMATHCrossRef Menshikov, M., Sidoravicius, V., & Vachkovskaia, M. (2001). A note on two-dimensional truncated long-range percolation. Advances in Applied Probability, 33, 912–929. MathSciNetMATHCrossRef
Zurück zum Zitat Mikosch, T., & Samorodnitsky, G. (2007). Scaling limits for cumulative input processes. Mathematics of Operations Research, 32(4), 890–918. MathSciNetMATHCrossRef Mikosch, T., & Samorodnitsky, G. (2007). Scaling limits for cumulative input processes. Mathematics of Operations Research, 32(4), 890–918. MathSciNetMATHCrossRef
Zurück zum Zitat Mikosch, T., Resnick, S., Rootzen, H., & Stegeman, A. (2002). Is network traffic approximated by stable Lévy motion or fractional Brownian motion? The Annals of Applied Probability, 12(1), 23–68. MathSciNetMATHCrossRef Mikosch, T., Resnick, S., Rootzen, H., & Stegeman, A. (2002). Is network traffic approximated by stable Lévy motion or fractional Brownian motion? The Annals of Applied Probability, 12(1), 23–68. MathSciNetMATHCrossRef
Zurück zum Zitat Mishura, Y. (2008). Lecture notes in mathematics: Vol. 1929. Stochastic calculus for fractional Brownian motion and related processes. Berlin: Springer. MATHCrossRef Mishura, Y. (2008). Lecture notes in mathematics: Vol. 1929. Stochastic calculus for fractional Brownian motion and related processes. Berlin: Springer. MATHCrossRef
Zurück zum Zitat Morana, C., & Beltratti, A. (2004). Structural change and long range dependence in volatility of exchange rates: either, neither or both. Journal of Empirical Finance, 11(4), 629–658. CrossRef Morana, C., & Beltratti, A. (2004). Structural change and long range dependence in volatility of exchange rates: either, neither or both. Journal of Empirical Finance, 11(4), 629–658. CrossRef
Zurück zum Zitat Nelson, D. B. (1990). Stationarity and persistence in the GARCH(1, 1) model. Econometric Theory, 6, 318–334. MathSciNetCrossRef Nelson, D. B. (1990). Stationarity and persistence in the GARCH(1, 1) model. Econometric Theory, 6, 318–334. MathSciNetCrossRef
Zurück zum Zitat Nelson, D. B., & Cao, C. Q. (1992). Inequality constraints in the univariate GARCH model. Journal of Business & Economic Statistics, 10(2), 229–235. Nelson, D. B., & Cao, C. Q. (1992). Inequality constraints in the univariate GARCH model. Journal of Business & Economic Statistics, 10(2), 229–235.
Zurück zum Zitat Newman, C. M., & Shulman, L. S. (1986). One dimensional \(1/\left| i-j\right| ^{s}\) percolation models: the existence of a transition for s≤2. Communications in Mathematical Physics, 104, 547–571. MathSciNetMATHCrossRef Newman, C. M., & Shulman, L. S. (1986). One dimensional \(1/\left| i-j\right| ^{s}\) percolation models: the existence of a transition for s≤2. Communications in Mathematical Physics, 104, 547–571. MathSciNetMATHCrossRef
Zurück zum Zitat Norros, I., Valkeila, E., & Virtamo, J. (1999). An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli, 5(4), 571–587. MathSciNetMATHCrossRef Norros, I., Valkeila, E., & Virtamo, J. (1999). An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli, 5(4), 571–587. MathSciNetMATHCrossRef
Zurück zum Zitat Onsager, L. (1944). Crystal statistics I: a two dimensional model with order-disorder transition. Physical Review, 65, 117–149. MathSciNetMATHCrossRef Onsager, L. (1944). Crystal statistics I: a two dimensional model with order-disorder transition. Physical Review, 65, 117–149. MathSciNetMATHCrossRef
Zurück zum Zitat Oppenheim, G., & Viano, M.-C. (2004). Aggregation of random parameters Ornstein–Uhlenbeck or AR processes: some convergence results. Journal of Time Series Analysis, 25, 335–350. MathSciNetMATHCrossRef Oppenheim, G., & Viano, M.-C. (2004). Aggregation of random parameters Ornstein–Uhlenbeck or AR processes: some convergence results. Journal of Time Series Analysis, 25, 335–350. MathSciNetMATHCrossRef
Zurück zum Zitat Parke, W. R. (1999). What is fractional integration? Review of Economics and Statistics, 81, 632–638. CrossRef Parke, W. R. (1999). What is fractional integration? Review of Economics and Statistics, 81, 632–638. CrossRef
Zurück zum Zitat Paxson, V., & Floyd, S. (1995). Wide-area traffic: the failure of Poisson modeling. IEEE/ACM Transactions on Networking, 3(3), 226–244. CrossRef Paxson, V., & Floyd, S. (1995). Wide-area traffic: the failure of Poisson modeling. IEEE/ACM Transactions on Networking, 3(3), 226–244. CrossRef
Zurück zum Zitat Paya, I., Duarte, A., & Holden, K. (2007). On the relationship between inflation persistence and temporal aggregation. Journal of Money, Credit, and Banking, 39, 1521–1531. CrossRef Paya, I., Duarte, A., & Holden, K. (2007). On the relationship between inflation persistence and temporal aggregation. Journal of Money, Credit, and Banking, 39, 1521–1531. CrossRef
Zurück zum Zitat Pietronero, L. & Tosatti, E. (Eds.) (1986). Fractals in physics. Amsterdam: North-Holland. Pietronero, L. & Tosatti, E. (Eds.) (1986). Fractals in physics. Amsterdam: North-Holland.
Zurück zum Zitat Pipiras, V., & Taqqu, M. S. (2000a). Integration questions related to fractional Brownian motion. Probability Theory and Related Fields, 118(2), 251–291. MathSciNetMATHCrossRef Pipiras, V., & Taqqu, M. S. (2000a). Integration questions related to fractional Brownian motion. Probability Theory and Related Fields, 118(2), 251–291. MathSciNetMATHCrossRef
Zurück zum Zitat Pipiras, V., & Taqqu, M. S. (2000b). The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion. Bernoulli, 6(4), 607–614. MathSciNetMATHCrossRef Pipiras, V., & Taqqu, M. S. (2000b). The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion. Bernoulli, 6(4), 607–614. MathSciNetMATHCrossRef
Zurück zum Zitat Pipiras, V., & Taqqu, M. S. (2003). Fractional calculus and its connect on to fractional Brownian motion. In Long range dependence (pp. 166–201). Basel: Birkhäuser. Pipiras, V., & Taqqu, M. S. (2003). Fractional calculus and its connect on to fractional Brownian motion. In Long range dependence (pp. 166–201). Basel: Birkhäuser.
Zurück zum Zitat Pipiras, V., & Taqqu, M. S. (2012, to appear). Long-range dependence of the two-dimensional Ising model at critical temperature. Fractals. Pipiras, V., & Taqqu, M. S. (2012, to appear). Long-range dependence of the two-dimensional Ising model at critical temperature. Fractals.
Zurück zum Zitat Pipiras, V., Taqqu, M. S., & Levy, J. B. (2004). Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed. Bernoulli, 10(1), 121–163. MathSciNetMATHCrossRef Pipiras, V., Taqqu, M. S., & Levy, J. B. (2004). Slow, fast and arbitrary growth conditions for renewal-reward processes when both the renewals and the rewards are heavy-tailed. Bernoulli, 10(1), 121–163. MathSciNetMATHCrossRef
Zurück zum Zitat Rachev, S. T., & Samorodnitsky, G. (2001). Long strange segments in a long-range dependent moving average. Stochastic Processes and Their Applications, 93(1), 119–148. MathSciNetMATHCrossRef Rachev, S. T., & Samorodnitsky, G. (2001). Long strange segments in a long-range dependent moving average. Stochastic Processes and Their Applications, 93(1), 119–148. MathSciNetMATHCrossRef
Zurück zum Zitat Racheva-Iotova, B., & Samorodnitsky, G. (2003). Long range dependence and heavy tails. In S. T. Rachev (Ed.), Handbook of heavy tailed distributions in finance (pp. 641–662). Amsterdam: Elsevier. Ch. 16. CrossRef Racheva-Iotova, B., & Samorodnitsky, G. (2003). Long range dependence and heavy tails. In S. T. Rachev (Ed.), Handbook of heavy tailed distributions in finance (pp. 641–662). Amsterdam: Elsevier. Ch. 16. CrossRef
Zurück zum Zitat Ray, B. K., & Tsay, R. S. (2000). Long-range dependence in daily stock volatilities. Journal of Business & Economic Statistics, 18(2), 254–262. Ray, B. K., & Tsay, R. S. (2000). Long-range dependence in daily stock volatilities. Journal of Business & Economic Statistics, 18(2), 254–262.
Zurück zum Zitat Resnick, S. I. (1992). Adventures in stochastic processes. Boston: Birkhäuser. MATH Resnick, S. I. (1992). Adventures in stochastic processes. Boston: Birkhäuser. MATH
Zurück zum Zitat Resnick, S. I. (1997). Heavy tail modelling and teletraffic data: special invited paper. The Annals of Statistics, 25(5), 1805–1869. MathSciNetMATHCrossRef Resnick, S. I. (1997). Heavy tail modelling and teletraffic data: special invited paper. The Annals of Statistics, 25(5), 1805–1869. MathSciNetMATHCrossRef
Zurück zum Zitat Resnick, S. I. (2007). Heavy-tail phenomena. New York: Springer. MATH Resnick, S. I. (2007). Heavy-tail phenomena. New York: Springer. MATH
Zurück zum Zitat Resnick, S. I., & van den Berg, E. (2000). Weak convergence of high-speed network traffic models. Journal of Applied Probability, 37(2), 575–597. MathSciNetCrossRef Resnick, S. I., & van den Berg, E. (2000). Weak convergence of high-speed network traffic models. Journal of Applied Probability, 37(2), 575–597. MathSciNetCrossRef
Zurück zum Zitat Robinson, P. M. (1978). Statistical inference for a random coefficient autoregressive model. Scandinavian Journal of Statistics, 5, 163–168. Robinson, P. M. (1978). Statistical inference for a random coefficient autoregressive model. Scandinavian Journal of Statistics, 5, 163–168.
Zurück zum Zitat Robinson, P. M. (1991). Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression. Journal of Econometrics, 47, 67–84. MathSciNetMATHCrossRef Robinson, P. M. (1991). Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression. Journal of Econometrics, 47, 67–84. MathSciNetMATHCrossRef
Zurück zum Zitat Robinson, P. M. (1994a). Time series with strong dependence. In C. A. Sims (Ed.), Advances in econometrics: sixth world congress (Vol. 1, pp. 47–95). Cambridge: Cambridge University Press. CrossRef Robinson, P. M. (1994a). Time series with strong dependence. In C. A. Sims (Ed.), Advances in econometrics: sixth world congress (Vol. 1, pp. 47–95). Cambridge: Cambridge University Press. CrossRef
Zurück zum Zitat Robinson, P. M., & Zaffaroni, P. (1997). Modelling nonlinearity and long memory in time series. Fields Institute Communications, 11, 161–170. MathSciNet Robinson, P. M., & Zaffaroni, P. (1997). Modelling nonlinearity and long memory in time series. Fields Institute Communications, 11, 161–170. MathSciNet
Zurück zum Zitat Robinson, P. M., & Zaffaroni, P. (1998). Nonlinear time series with long memory: a model for stochastic volatility. Journal of Statistical Planning and Inference, 68, 359–371. MathSciNetMATHCrossRef Robinson, P. M., & Zaffaroni, P. (1998). Nonlinear time series with long memory: a model for stochastic volatility. Journal of Statistical Planning and Inference, 68, 359–371. MathSciNetMATHCrossRef
Zurück zum Zitat Rodriguez-Iturbe, I., & Rinaldo, A. (1997). Fractal river basins. Cambridge: Cambridge University Press. Rodriguez-Iturbe, I., & Rinaldo, A. (1997). Fractal river basins. Cambridge: Cambridge University Press.
Zurück zum Zitat Rolls, D. A. (2010). Reduced long-range dependence combining Poisson bursts with on–off sources. Brazilian Journal of Probability and Statistics, 24(3), 479–501. MathSciNetCrossRef Rolls, D. A. (2010). Reduced long-range dependence combining Poisson bursts with on–off sources. Brazilian Journal of Probability and Statistics, 24(3), 479–501. MathSciNetCrossRef
Zurück zum Zitat Ruelle, D. (1968). Statistical mechanics of one-dimensional lattice gas. Communications in Mathematical Physics, 9(4), 267–278. MathSciNetMATHCrossRef Ruelle, D. (1968). Statistical mechanics of one-dimensional lattice gas. Communications in Mathematical Physics, 9(4), 267–278. MathSciNetMATHCrossRef
Zurück zum Zitat Ruelle, D. (1970). Superstable interactions in classical statistical mechanics. Communications in Mathematical Physics, 18, 127–159. MathSciNetMATHCrossRef Ruelle, D. (1970). Superstable interactions in classical statistical mechanics. Communications in Mathematical Physics, 18, 127–159. MathSciNetMATHCrossRef
Zurück zum Zitat Samorodnitsky, G. (2002). Long range dependence, heavy tails and rare events. MaPhySto, Centre for Mathematical Physics and Stochastics, Aarhus. Lecture Notes. Samorodnitsky, G. (2002). Long range dependence, heavy tails and rare events. MaPhySto, Centre for Mathematical Physics and Stochastics, Aarhus. Lecture Notes.
Zurück zum Zitat Samorodnitsky, G. (2004). Extreme value theory, ergodic theory, and the boundary between short memory and long memory for stationary stable processes. Annals of Probability, 32, 1438–1468. MathSciNetMATHCrossRef Samorodnitsky, G. (2004). Extreme value theory, ergodic theory, and the boundary between short memory and long memory for stationary stable processes. Annals of Probability, 32, 1438–1468. MathSciNetMATHCrossRef
Zurück zum Zitat Samorodnitsky, G., & Taqqu, M. S. (1994). Stable non-Gaussian random processes: stochastic models with infinite variance. New York: Chapman & Hall/CRC Press. MATH Samorodnitsky, G., & Taqqu, M. S. (1994). Stable non-Gaussian random processes: stochastic models with infinite variance. New York: Chapman & Hall/CRC Press. MATH
Zurück zum Zitat Scharth, M., & Medeiros, M. C. (2009). Asymmetric effects and long memory in the volatility of Dow Jones stocks. International Journal of Forecasting, 25, 304–327. CrossRef Scharth, M., & Medeiros, M. C. (2009). Asymmetric effects and long memory in the volatility of Dow Jones stocks. International Journal of Forecasting, 25, 304–327. CrossRef
Zurück zum Zitat Scheuring, I. (1991). The fractal nature of vegetation and the species-area relation. Theoretical Population Biology, 39, 170–177. MathSciNetCrossRef Scheuring, I. (1991). The fractal nature of vegetation and the species-area relation. Theoretical Population Biology, 39, 170–177. MathSciNetCrossRef
Zurück zum Zitat Simos, T. (2008). The exact discrete model of a system of linear stochastic differential equations driven by fractional noise. Journal of Time Series Analysis, 29, 1019–1031. MathSciNetMATHCrossRef Simos, T. (2008). The exact discrete model of a system of linear stochastic differential equations driven by fractional noise. Journal of Time Series Analysis, 29, 1019–1031. MathSciNetMATHCrossRef
Zurück zum Zitat Sokal, A. D. (1981). Existence of compatible families of proper regular conditional probabilities. Probability Theory and Related Fields, 56(4), 537–548. MathSciNetMATH Sokal, A. D. (1981). Existence of compatible families of proper regular conditional probabilities. Probability Theory and Related Fields, 56(4), 537–548. MathSciNetMATH
Zurück zum Zitat Souza, L. R. (2005). A note on Chambers’s long memory and aggregation in macroeconomic time series. International Economic Review, 46, 1059–1062. CrossRef Souza, L. R. (2005). A note on Chambers’s long memory and aggregation in macroeconomic time series. International Economic Review, 46, 1059–1062. CrossRef
Zurück zum Zitat Souza, L. R. (2007). Temporal aggregation and bandwidth selection in estimating long memory. Journal of Time Series Analysis, 28(5), 701–722. MathSciNetMATHCrossRef Souza, L. R. (2007). Temporal aggregation and bandwidth selection in estimating long memory. Journal of Time Series Analysis, 28(5), 701–722. MathSciNetMATHCrossRef
Zurück zum Zitat Souza, L. R., & Smith, J. (2004). Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study. International Journal of Forecasting, 20, 487–502. CrossRef Souza, L. R., & Smith, J. (2004). Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study. International Journal of Forecasting, 20, 487–502. CrossRef
Zurück zum Zitat Stanley, H. E. (1971). Introduction to phase transitions and critical phenomena. Oxford: Oxford University Press. Stanley, H. E. (1971). Introduction to phase transitions and critical phenomena. Oxford: Oxford University Press.
Zurück zum Zitat Stanley, H. E. (1987). Introduction to phase transitions and critical phenomena. Oxford: Oxford University Press. Stanley, H. E. (1987). Introduction to phase transitions and critical phenomena. Oxford: Oxford University Press.
Zurück zum Zitat Stauffer, D., & Aharony, A. (1994). Introduction to percolation theory. Boca Raton: CRC Press. Stauffer, D., & Aharony, A. (1994). Introduction to percolation theory. Boca Raton: CRC Press.
Zurück zum Zitat Stoev, S., & Taqqu, M. S. (2005a). Path properties of the linear multifractional stable motion. Fractals, 13(2), 157–178. MathSciNetCrossRef Stoev, S., & Taqqu, M. S. (2005a). Path properties of the linear multifractional stable motion. Fractals, 13(2), 157–178. MathSciNetCrossRef
Zurück zum Zitat Stoev, S., & Taqqu, M. S. (2005b). Asymptotic self-similarity and wavelet estimation for long-range dependent fractional autoregressive integrated moving average time series with stable innovations. Journal of Time Series Analysis, 26(2), 211–249. MathSciNetMATHCrossRef Stoev, S., & Taqqu, M. S. (2005b). Asymptotic self-similarity and wavelet estimation for long-range dependent fractional autoregressive integrated moving average time series with stable innovations. Journal of Time Series Analysis, 26(2), 211–249. MathSciNetMATHCrossRef
Zurück zum Zitat Stout, W. F. (1974). Almost sure convergence. New York: Academic Press. MATH Stout, W. F. (1974). Almost sure convergence. New York: Academic Press. MATH
Zurück zum Zitat Suquet, C. (1996). Tightness in Schauder decomposable Banach spaces. Translations—American Mathematical Society, 193(2), 201–224. MathSciNet Suquet, C. (1996). Tightness in Schauder decomposable Banach spaces. Translations—American Mathematical Society, 193(2), 201–224. MathSciNet
Zurück zum Zitat Surgailis, D. (2002). Stable limits of empirical processes of moving averages with infinite variance. Stochastic Processes and Their Applications, 100, 255–274. MathSciNetMATHCrossRef Surgailis, D. (2002). Stable limits of empirical processes of moving averages with infinite variance. Stochastic Processes and Their Applications, 100, 255–274. MathSciNetMATHCrossRef
Zurück zum Zitat Surgailis, D. (2008). A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares. Advances in Applied Probability, 40(4), 1198–1222. MathSciNetMATHCrossRef Surgailis, D. (2008). A quadratic ARCH(∞) model with long memory and Lévy stable behavior of squares. Advances in Applied Probability, 40(4), 1198–1222. MathSciNetMATHCrossRef
Zurück zum Zitat Surgailis, D., & Viano, M.-C. (2002). Long memory properties and covariance structure of the EGARCH model. ESAIM: Probability and Statistics, 6, 311–329. MathSciNetCrossRef Surgailis, D., & Viano, M.-C. (2002). Long memory properties and covariance structure of the EGARCH model. ESAIM: Probability and Statistics, 6, 311–329. MathSciNetCrossRef
Zurück zum Zitat Sznitman, A. S. (2010). Vacant set of random interlacements and percolation. Annals of Mathematics, 2039–2087. Sznitman, A. S. (2010). Vacant set of random interlacements and percolation. Annals of Mathematics, 2039–2087.
Zurück zum Zitat Taqqu, M. S. (2002). The modelling of ethernet data and of signals that are heavy-tailed with infinite variance. Large structured models in applied sciences; challenges for statistics (Grimstad, 2000). Scandinavian Journal of Statistics, 29(2), 273–295. MathSciNetMATHCrossRef Taqqu, M. S. (2002). The modelling of ethernet data and of signals that are heavy-tailed with infinite variance. Large structured models in applied sciences; challenges for statistics (Grimstad, 2000). Scandinavian Journal of Statistics, 29(2), 273–295. MathSciNetMATHCrossRef
Zurück zum Zitat Taqqu, M. S., & Levy, J. B. (1986). Using renewal processes to generate long-range dependence and high variability. In Progr. Probab. Statist.: Vol. 11. Dependence in probability and statistics, Oberwolfach, 1985 (pp. 73–89). Boston: Birkhäuser Boston. Taqqu, M. S., & Levy, J. B. (1986). Using renewal processes to generate long-range dependence and high variability. In Progr. Probab. Statist.: Vol. 11. Dependence in probability and statistics, Oberwolfach, 1985 (pp. 73–89). Boston: Birkhäuser Boston.
Zurück zum Zitat Taqqu, M. S., & Wolpert, R. L. (1983). Infinite variance self-similar processes subordinate to a Poisson measure. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 62(1), 53–72. MathSciNetMATHCrossRef Taqqu, M. S., & Wolpert, R. L. (1983). Infinite variance self-similar processes subordinate to a Poisson measure. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 62(1), 53–72. MathSciNetMATHCrossRef
Zurück zum Zitat Taqqu, M. S., Willinger, W., & Sherman, R. (1997). Proof of a fundamental result in self-similar traffic modeling. Computer Communication Review, 27, 5–23. CrossRef Taqqu, M. S., Willinger, W., & Sherman, R. (1997). Proof of a fundamental result in self-similar traffic modeling. Computer Communication Review, 27, 5–23. CrossRef
Zurück zum Zitat Teles, P., Wei, W. W. S., & Crato, N. (1999). The use of aggregate time series in testing for long memory. In Bulletin of the international statistical institute, 52nd session (pp. 341–342). Teles, P., Wei, W. W. S., & Crato, N. (1999). The use of aggregate time series in testing for long memory. In Bulletin of the international statistical institute, 52nd session (pp. 341–342).
Zurück zum Zitat Teugels, J. L. (1968). Renewal theorems when the first or the second moment is infinite. The Annals of Mathematical Statistics, 39, 1210–1219. MathSciNetMATHCrossRef Teugels, J. L. (1968). Renewal theorems when the first or the second moment is infinite. The Annals of Mathematical Statistics, 39, 1210–1219. MathSciNetMATHCrossRef
Zurück zum Zitat Thavaneswaran, A., & Peiris, M. S. (2001). Recursive estimation for regression with infinite variance fractional ARIMA noise. Mathematical and Computer Modelling, 34(9–11), 1133–1137. MathSciNetMATHCrossRef Thavaneswaran, A., & Peiris, M. S. (2001). Recursive estimation for regression with infinite variance fractional ARIMA noise. Mathematical and Computer Modelling, 34(9–11), 1133–1137. MathSciNetMATHCrossRef
Zurück zum Zitat Tsai, H. (2006). Quasi-maximum likelihood estimation of long-memory limiting aggregate processes. Statistica Sinica, 16, 213–226. MathSciNetMATH Tsai, H. (2006). Quasi-maximum likelihood estimation of long-memory limiting aggregate processes. Statistica Sinica, 16, 213–226. MathSciNetMATH
Zurück zum Zitat Tsai, H. (2009). On continuous-time autoregressive fractionally integrated moving average processes. Bernoulli, 15(1), 178–194. MathSciNetMATHCrossRef Tsai, H. (2009). On continuous-time autoregressive fractionally integrated moving average processes. Bernoulli, 15(1), 178–194. MathSciNetMATHCrossRef
Zurück zum Zitat Tsai, H., & Chan, K. S. (2005a). Temporal aggregation of stationary and nonstationary discrete-time processes. Journal of Time Series Analysis, 26(4), 613–624. MathSciNetMATHCrossRef Tsai, H., & Chan, K. S. (2005a). Temporal aggregation of stationary and nonstationary discrete-time processes. Journal of Time Series Analysis, 26(4), 613–624. MathSciNetMATHCrossRef
Zurück zum Zitat Tsai, H., & Chan, K. S. (2005b). Temporal aggregation of stationary and non-stationary continuous-time processes. Scandinavian Journal of Statistics, 32, 583–597. MathSciNetMATHCrossRef Tsai, H., & Chan, K. S. (2005b). Temporal aggregation of stationary and non-stationary continuous-time processes. Scandinavian Journal of Statistics, 32, 583–597. MathSciNetMATHCrossRef
Zurück zum Zitat Tsai, H., & Chan, K. S. (2005c). Quasi-maximum likelihood estimation for a class of continuous-time long-memory processes. Journal of Time Series Analysis, 26, 691–713. MathSciNetMATHCrossRef Tsai, H., & Chan, K. S. (2005c). Quasi-maximum likelihood estimation for a class of continuous-time long-memory processes. Journal of Time Series Analysis, 26, 691–713. MathSciNetMATHCrossRef
Zurück zum Zitat Tsai, H., & Chan, K. S. (2005d). Maximum likelihood estimation of linear continuous-time long memory processes with discrete time data. Journal of the Royal Statistical Society, Series B, 67, 703–716. MathSciNetMATHCrossRef Tsai, H., & Chan, K. S. (2005d). Maximum likelihood estimation of linear continuous-time long memory processes with discrete time data. Journal of the Royal Statistical Society, Series B, 67, 703–716. MathSciNetMATHCrossRef
Zurück zum Zitat Turcotte, D. L. (1997). Fractals and chaos in geology and geophysics. Cambridge: Cambridge University Press. CrossRef Turcotte, D. L. (1997). Fractals and chaos in geology and geophysics. Cambridge: Cambridge University Press. CrossRef
Zurück zum Zitat Vanderzande, C. (1998). Lattice models of polymers. Cambridge lecture notes in physics. Cambridge: Cambridge University Press. MATHCrossRef Vanderzande, C. (1998). Lattice models of polymers. Cambridge lecture notes in physics. Cambridge: Cambridge University Press. MATHCrossRef
Zurück zum Zitat Viano, M. C., Deniau, C., & Oppenheim, G. (1994). Continuous-time fractional ARMA processes. Statistics & Probability Letters, 21, 323–336. MathSciNetMATHCrossRef Viano, M. C., Deniau, C., & Oppenheim, G. (1994). Continuous-time fractional ARMA processes. Statistics & Probability Letters, 21, 323–336. MathSciNetMATHCrossRef
Zurück zum Zitat Vicsek, T. (1992). Fractal growth phenomena (2nd ed.). River Edge: World Scientific. MATHCrossRef Vicsek, T. (1992). Fractal growth phenomena (2nd ed.). River Edge: World Scientific. MATHCrossRef
Zurück zum Zitat Walters, P. (1989). Graduate texts in mathematics: Vol. 79. An introduction to ergodic theory. New York: Springer. Walters, P. (1989). Graduate texts in mathematics: Vol. 79. An introduction to ergodic theory. New York: Springer.
Zurück zum Zitat Whistler, D. E. N. (1990). Semiparametric models of daily and intra-daily exchange rate volatility. Ph.D. dissertation, Univ, London. Whistler, D. E. N. (1990). Semiparametric models of daily and intra-daily exchange rate volatility. Ph.D. dissertation, Univ, London.
Zurück zum Zitat Willinger, W., Paxson, V., Riedi, R. H., & Taqqu, M. S. (2003). Long-range dependence and data network traffic. In Theory and applications of long-range dependence (pp. 373–407). Boston: Birkhäuser Boston. 2003. Willinger, W., Paxson, V., Riedi, R. H., & Taqqu, M. S. (2003). Long-range dependence and data network traffic. In Theory and applications of long-range dependence (pp. 373–407). Boston: Birkhäuser Boston. 2003.
Zurück zum Zitat Xie, H. (1993). Fractals in rock mechanics. Rotterdam: Balkema. Xie, H. (1993). Fractals in rock mechanics. Rotterdam: Balkema.
Zurück zum Zitat Zaffaroni, P. (2004). Contemporaneous aggregation of linear dynamic models in large economies. Journal of Econometrics, 120, 75–102. MathSciNetCrossRef Zaffaroni, P. (2004). Contemporaneous aggregation of linear dynamic models in large economies. Journal of Econometrics, 120, 75–102. MathSciNetCrossRef
Zurück zum Zitat Zaffaroni, P. (2007a). Aggregation and memory of models of changing volatility. Journal of Econometrics, 136, 237–249. MathSciNetCrossRef Zaffaroni, P. (2007a). Aggregation and memory of models of changing volatility. Journal of Econometrics, 136, 237–249. MathSciNetCrossRef
Zurück zum Zitat Zähle, M. (1998). Integration with respect to fractal functions and stochastic calculus. Probability Theory and Related Fields, 111(3), 333–374. MathSciNetMATHCrossRef Zähle, M. (1998). Integration with respect to fractal functions and stochastic calculus. Probability Theory and Related Fields, 111(3), 333–374. MathSciNetMATHCrossRef
Metadaten
Titel
Origins and Generation of Long Memory
verfasst von
Jan Beran
Yuanhua Feng
Sucharita Ghosh
Rafal Kulik
Copyright-Jahr
2013
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-35512-7_2

Premium Partner