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2019 | OriginalPaper | Buchkapitel

15. Non-Parametric and Flexible Time Series Estimators

verfasst von : Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner

Erschienen in: Statistics of Financial Markets

Verlag: Springer International Publishing

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Abstract

With the analysis of (financial) time series, one of the most important goals is to produce forecasts. Using past data one can argue about the future mean, the future volatility and so on; however, a flexible method of producing such estimates will be introduced in this chapter.

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Literatur
Zurück zum Zitat Ango Nze, P. (1992). Critères d’ergodicité de quelques modèles à représentation markovienne. Technical Report 315, ser. 1. Paris: C.R. Acad. Sci. Ango Nze, P. (1992). Critères d’ergodicité de quelques modèles à représentation markovienne. Technical Report 315, ser. 1. Paris: C.R. Acad. Sci.
Zurück zum Zitat Bossaerts, P., & Hillion, P. (1993). Test of a general equilibrium stock option pricing model. Mathematical Finance, 3, 311–347.CrossRef Bossaerts, P., & Hillion, P. (1993). Test of a general equilibrium stock option pricing model. Mathematical Finance, 3, 311–347.CrossRef
Zurück zum Zitat Carroll, R. J., Härdle, W., & Mammen, E. (2002). Estimation in an additive model when the components are linked parametrically. Econometric Theory, 18, 886–912.MathSciNetCrossRef Carroll, R. J., Härdle, W., & Mammen, E. (2002). Estimation in an additive model when the components are linked parametrically. Econometric Theory, 18, 886–912.MathSciNetCrossRef
Zurück zum Zitat Chan, K., & Tong, H. (1985). On the use of deterministic Lyapunov functions for the ergodicity of stochastic difference equations. Advanced Applied Probability, 17, 666–678.MathSciNetCrossRef Chan, K., & Tong, H. (1985). On the use of deterministic Lyapunov functions for the ergodicity of stochastic difference equations. Advanced Applied Probability, 17, 666–678.MathSciNetCrossRef
Zurück zum Zitat Chen, R., & Tsay, R. S. (1993a). Functional-coefficient autoregressive models. Journal of the American Statistical Association, 88, 298–308.MathSciNetMATH Chen, R., & Tsay, R. S. (1993a). Functional-coefficient autoregressive models. Journal of the American Statistical Association, 88, 298–308.MathSciNetMATH
Zurück zum Zitat Chen, R., & Tsay, R. S. (1993b). Nonlinear additive ARX models. Journal of the American Statistical Association, 88, 955–967.CrossRef Chen, R., & Tsay, R. S. (1993b). Nonlinear additive ARX models. Journal of the American Statistical Association, 88, 955–967.CrossRef
Zurück zum Zitat Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74, 829–836.MathSciNetCrossRef Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74, 829–836.MathSciNetCrossRef
Zurück zum Zitat Collomb, G. (1984). Propriétés de convergence presque complète du prédicteur à noyau. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 66, 441–460.MathSciNetCrossRef Collomb, G. (1984). Propriétés de convergence presque complète du prédicteur à noyau. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 66, 441–460.MathSciNetCrossRef
Zurück zum Zitat Diebolt, J., & Guégan, D. (1990). Probabilistic properties of the general nonlinear autoregressive process of order one. Technical Report 128. Paris: Université de Paris VI. Diebolt, J., & Guégan, D. (1990). Probabilistic properties of the general nonlinear autoregressive process of order one. Technical Report 128. Paris: Université de Paris VI.
Zurück zum Zitat Doukhan, P., & Ghindès, M. (1980). Estimation dans le processus xn+1 = f(xn) + εn+1. C.R. Acad. Sci. Paris, Sér. A, 297, 61–64.MATH Doukhan, P., & Ghindès, M. (1980). Estimation dans le processus xn+1 = f(xn) + εn+1. C.R. Acad. Sci. Paris, Sér. A, 297, 61–64.MATH
Zurück zum Zitat Doukhan, P., & Ghindès, M. (1981). Processus autorégressifs non-linéaires. C.R. Acad. Sci. Paris, Sér. A, 290, 921–923.MATH Doukhan, P., & Ghindès, M. (1981). Processus autorégressifs non-linéaires. C.R. Acad. Sci. Paris, Sér. A, 290, 921–923.MATH
Zurück zum Zitat Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008.MathSciNetCrossRef Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008.MathSciNetCrossRef
Zurück zum Zitat Engle, R. F., & Gonzalez-Rivera, G. (1991). Semiparametric ARCH models. Journal of Business and Economic Statistics, 9, 345–360. Engle, R. F., & Gonzalez-Rivera, G. (1991). Semiparametric ARCH models. Journal of Business and Economic Statistics, 9, 345–360.
Zurück zum Zitat Fan, J., & Gijbels, I. (1996). Local polynomial modeling and its application – Theory and methodologies. Chapman and Hall.MATH Fan, J., & Gijbels, I. (1996). Local polynomial modeling and its application – Theory and methodologies. Chapman and Hall.MATH
Zurück zum Zitat Fan, J., & Yao, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika, 85, 645–660.MathSciNetCrossRef Fan, J., & Yao, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika, 85, 645–660.MathSciNetCrossRef
Zurück zum Zitat Fan, J., & Yao, Q. (2003). Nonlinear time series: Nonparametric and parametric methods. New York: Springer-Verlag.CrossRef Fan, J., & Yao, Q. (2003). Nonlinear time series: Nonparametric and parametric methods. New York: Springer-Verlag.CrossRef
Zurück zum Zitat Föllmer, H., & Schweizer, M. (1991). Hedging of contingent claims under incomplete information. In M. H. A. Davis, & R. J. Elliot (Eds.), Applied stochastic analysis (pp. 389–414). London: Gordon and Breach. Föllmer, H., & Schweizer, M. (1991). Hedging of contingent claims under incomplete information. In M. H. A. Davis, & R. J. Elliot (Eds.), Applied stochastic analysis (pp. 389–414). London: Gordon and Breach.
Zurück zum Zitat Föllmer, H., & Sondermann, D. (1991). Hedging of non-redundant contingent claims. In W. Hildenbrand, & A. Mas-Colell (Eds.), Contributions to mathematical economics (pp. 205–223). North Holland: Amsterdam. Föllmer, H., & Sondermann, D. (1991). Hedging of non-redundant contingent claims. In W. Hildenbrand, & A. Mas-Colell (Eds.), Contributions to mathematical economics (pp. 205–223). North Holland: Amsterdam.
Zurück zum Zitat Franke, J. (1999). Nonlinear and nonparametric methods for analyzing financial time series. In P. Kall, & H.-J. Luethi (Eds.), Operation research proceedings 98, Heidelberg: Springer-Verlag. Franke, J. (1999). Nonlinear and nonparametric methods for analyzing financial time series. In P. Kall, & H.-J. Luethi (Eds.), Operation research proceedings 98, Heidelberg: Springer-Verlag.
Zurück zum Zitat Franke, J., Härdle, W., & Kreiss, J. (2003). Nonparametric estimation in a stochastic volatility model. Recent Advances and Trends in Nonparametric Statistics, 303–314. Franke, J., Härdle, W., & Kreiss, J. (2003). Nonparametric estimation in a stochastic volatility model. Recent Advances and Trends in Nonparametric Statistics, 303–314.
Zurück zum Zitat Franke, J., Kreiss, J., & Mammen, E. (2002). Bootstrap of kernel smoothing in nonlinear time series. Bernoulli, 8(1), 1–37.MathSciNetMATH Franke, J., Kreiss, J., & Mammen, E. (2002). Bootstrap of kernel smoothing in nonlinear time series. Bernoulli, 8(1), 1–37.MathSciNetMATH
Zurück zum Zitat Glosten, L., Jagannathan, R., & Runkle, D. (1993). On the relationship between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779–1801.CrossRef Glosten, L., Jagannathan, R., & Runkle, D. (1993). On the relationship between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779–1801.CrossRef
Zurück zum Zitat Gouriéroux, C., & Monfort, A. (1992). Qualitative threshold ARCH models. Journal of Econometrics, 52, 159–199.MathSciNetCrossRef Gouriéroux, C., & Monfort, A. (1992). Qualitative threshold ARCH models. Journal of Econometrics, 52, 159–199.MathSciNetCrossRef
Zurück zum Zitat Gregory, A. (1989). A nonparametric test for autoregressive conditional heteroscedasticity: A Markov chain approach. Journal of Business and Economic Statistics, 7, 107–115. Gregory, A. (1989). A nonparametric test for autoregressive conditional heteroscedasticity: A Markov chain approach. Journal of Business and Economic Statistics, 7, 107–115.
Zurück zum Zitat Hafner, C. (1998). Estimating high frequency foreign exchange rate volatility with nonparametric ARCH models. Journal of Statistical Planning and Inference, 68, 247–269.MathSciNetCrossRef Hafner, C. (1998). Estimating high frequency foreign exchange rate volatility with nonparametric ARCH models. Journal of Statistical Planning and Inference, 68, 247–269.MathSciNetCrossRef
Zurück zum Zitat Härdle, W. (1990). Applied nonparametric regression. Cambridge: Cambridge University Press.CrossRef Härdle, W. (1990). Applied nonparametric regression. Cambridge: Cambridge University Press.CrossRef
Zurück zum Zitat Härdle, W., & Hafner, C. (2000). Discrete time option pricing with flexible volatility estimation. Finance and Stochastics, 4, 189–207.MathSciNetCrossRef Härdle, W., & Hafner, C. (2000). Discrete time option pricing with flexible volatility estimation. Finance and Stochastics, 4, 189–207.MathSciNetCrossRef
Zurück zum Zitat Härdle, W., Lütkepohl, H., & Chen, R. (1997). Nonparametric time series analysis. International Statistical Review, 12, 153–172.MATH Härdle, W., Lütkepohl, H., & Chen, R. (1997). Nonparametric time series analysis. International Statistical Review, 12, 153–172.MATH
Zurück zum Zitat Härdle, W., Müller, M., Sperlich, S., & Werwatz, A. (2004). Non- and semiparametric modelling. Heidelberg: Springer-Verlag.CrossRef Härdle, W., Müller, M., Sperlich, S., & Werwatz, A. (2004). Non- and semiparametric modelling. Heidelberg: Springer-Verlag.CrossRef
Zurück zum Zitat Härdle, W., & Tsybakov, A. (1997). Local polynomial estimation of the volatility function. Journal of Econometrics, 81, 223–242.MathSciNetCrossRef Härdle, W., & Tsybakov, A. (1997). Local polynomial estimation of the volatility function. Journal of Econometrics, 81, 223–242.MathSciNetCrossRef
Zurück zum Zitat Härdle, W., Tsybakov, A., & Yang, L. (1996). Nonparametric vector autoregression. Journal of Statistical Planning and Inference, 68, 221–245.MathSciNetCrossRef Härdle, W., Tsybakov, A., & Yang, L. (1996). Nonparametric vector autoregression. Journal of Statistical Planning and Inference, 68, 221–245.MathSciNetCrossRef
Zurück zum Zitat Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281–300.CrossRef Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281–300.CrossRef
Zurück zum Zitat Katkovnik, V. (1979). Linear and nonlinear methods for nonparametric regression analysis (in Russian). Avtomatika i Telemehanika, 35–46. Katkovnik, V. (1979). Linear and nonlinear methods for nonparametric regression analysis (in Russian). Avtomatika i Telemehanika, 35–46.
Zurück zum Zitat Katkovnik, V. (1985). Nonparametric identification and data smoothing. Nauka.MATH Katkovnik, V. (1985). Nonparametric identification and data smoothing. Nauka.MATH
Zurück zum Zitat McKeague, I., & Zhang, M. (1994). Identification of nonlinear time series from first order cumulative characteristics. Annals of Statistics, 22, 495–514.MathSciNetCrossRef McKeague, I., & Zhang, M. (1994). Identification of nonlinear time series from first order cumulative characteristics. Annals of Statistics, 22, 495–514.MathSciNetCrossRef
Zurück zum Zitat Melino, A., & Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45, 239–265.CrossRef Melino, A., & Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45, 239–265.CrossRef
Zurück zum Zitat Mokkadem, A. (1987). Sur un modèle autorégressif nonlinéaire. ergodicité et ergodicité géometrique. Journal of Time Series Analysis, 8, 195–204.MathSciNetCrossRef Mokkadem, A. (1987). Sur un modèle autorégressif nonlinéaire. ergodicité et ergodicité géometrique. Journal of Time Series Analysis, 8, 195–204.MathSciNetCrossRef
Zurück zum Zitat Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59, 347–370.MathSciNetCrossRef Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59, 347–370.MathSciNetCrossRef
Zurück zum Zitat Rabemananjara, R., & Zakoian, J. M. (1993). Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics, 8, 31–49.CrossRef Rabemananjara, R., & Zakoian, J. M. (1993). Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics, 8, 31–49.CrossRef
Zurück zum Zitat Renault, E., & Touzi, N. (1996). Option hedging and implied volatilities in a stochastic volatility model. Mathematical Finance, 6, 277–302.CrossRef Renault, E., & Touzi, N. (1996). Option hedging and implied volatilities in a stochastic volatility model. Mathematical Finance, 6, 277–302.CrossRef
Zurück zum Zitat Robinson, P. (1983). Non-parametric estimation for time series models. Journal of Time Series Analysis, 4, 185–208.MathSciNetCrossRef Robinson, P. (1983). Non-parametric estimation for time series models. Journal of Time Series Analysis, 4, 185–208.MathSciNetCrossRef
Zurück zum Zitat Robinson, P. (1984). Robust nonparametric autoregression. In J. Franke, W. Härdle, & Martin (Eds.), Robust and nonlinear time series analysis. Heidelberg: Springer-Verlag. Robinson, P. (1984). Robust nonparametric autoregression. In J. Franke, W. Härdle, & Martin (Eds.), Robust and nonlinear time series analysis. Heidelberg: Springer-Verlag.
Zurück zum Zitat Tong, H. (1983). Threshold models in nonlinear time series analysis, Vol. 21 of Lecture notes in statistics. Heidelberg: Springer-Verlag.CrossRef Tong, H. (1983). Threshold models in nonlinear time series analysis, Vol. 21 of Lecture notes in statistics. Heidelberg: Springer-Verlag.CrossRef
Zurück zum Zitat Tsybakov, A. (1986). Robust reconstruction of functions by the local-approximation method. Problems of Information Transmission, 22, 133–146.MathSciNetMATH Tsybakov, A. (1986). Robust reconstruction of functions by the local-approximation method. Problems of Information Transmission, 22, 133–146.MathSciNetMATH
Zurück zum Zitat Vieu, P. (1995). Order choice in nonlinear autoregressive models, Discussion Paper, Laboratoire de Statistique et Probabilités, Université Toulouse.MATH Vieu, P. (1995). Order choice in nonlinear autoregressive models, Discussion Paper, Laboratoire de Statistique et Probabilités, Université Toulouse.MATH
Zurück zum Zitat Wiggins, J. (1987). Option values under stochastic volatility: Theory and empirical estimates. Journal of Financial Economics, 19.CrossRef Wiggins, J. (1987). Option values under stochastic volatility: Theory and empirical estimates. Journal of Financial Economics, 19.CrossRef
Zurück zum Zitat Yang, L., Härdle, W., & Nielsen, J. (1999). Nonparametric autoregression with multiplicative volatility and additive mean. Journal of Time Series Analysis, 20(5), 579–604.MathSciNetCrossRef Yang, L., Härdle, W., & Nielsen, J. (1999). Nonparametric autoregression with multiplicative volatility and additive mean. Journal of Time Series Analysis, 20(5), 579–604.MathSciNetCrossRef
Zurück zum Zitat Zakoian, J. (1994). Threshold heteroskedastic functions. Journal of Economic Dynamics and Control, 18, 931–955.CrossRef Zakoian, J. (1994). Threshold heteroskedastic functions. Journal of Economic Dynamics and Control, 18, 931–955.CrossRef
Metadaten
Titel
Non-Parametric and Flexible Time Series Estimators
verfasst von
Jürgen Franke
Wolfgang Karl Härdle
Christian Matthias Hafner
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-13751-9_15