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Semiparametric Estimation of the Intensity of Long Memory in Conditional Heteroskedasticity

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Abstract

The paper is concerned with the estimation of the long memory parameter in a conditionally heteroskedastic model proposed by Giraitis et al. (1999b). We consider estimation methods based on the partial sums of the squared observations, which are similar in spirit to the classical R / S analysis, as well as spectral domain approximate maximum likelihood estimators. We review relevant theoretical results and present an empirical simulation study.

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References

  • Baillie, R. T., Bollerslev, T. and Mikkelsen, H. O.: Fractionally integrated generalized autoregressive conditional heteroskedasticity, J. Economet. 74 (1996), 3–30.

    Google Scholar 

  • Beran, J.: Statistics for Long-Memory Processes, Chapman & Hall, New York, 1994.

    Google Scholar 

  • Campbell, J. Y., Lo, A.W. and MacKinlay, A. C.: The Econometrics of Financial Markets, Princeton University Press, Princeton, 1997.

    Google Scholar 

  • Delgado, M. A. and Robinson, P. M.: Optimal spectral bandwidth for long memory, Statistica Sinica 6 (1996), 97–112.

    Google Scholar 

  • Ding, Z. and Granger, C. W. J.: Modeling volatility persistence of speculative returns: a new approach, J. Economet. 73 (1996), 185–215.

    Google Scholar 

  • Giraitis, L., Kokoszka, P. and Leipus, R.: Stationary ARCH models: dependence structure and Central Limit Theorem, Econometric Theory 16 (2000), 3–22.

    Google Scholar 

  • Giraitis, L., Kokoszka, P. and Leipus, R.: Rescaled variance and related tests for long-memory in volatility and levels, Preprint, 1999a.

  • Giraitis, L., Robinson, P. and Surgailis, D.: A model for long memory conditional heteroskedasticity, Ann. Appl. Probab. 1999b, in press.

  • Giraitis, L., Robinson, P. and Surgailis, D.: Variance-type estimation of long memory, Stochastic Processes and Their Applications 80, 1–24.

  • Hurst, H.: Long term storage capacity of reservoirs, Transac. Amer. Soc. Civil Engrs 116 (1951), 770–799.

    Google Scholar 

  • Kokoszka, P. and Leipus, R.: Change-point estimation in ARCH models, Bernoulli 6 (2000), in press.

  • Künsch, H.: Statistical aspects of self-similar processes, in Yu. A. Prohorov and V V. Sazonov (eds), Proceedings of the 1st World Congress of the Bernoulli Society, vol. 1, VNU Science Press, Utrecht, 1987, pp. 67–74.

    Google Scholar 

  • Kwiatkowski, D., Phillips, P. C. B., Schmidt, P. and Shin, Y.: Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J. Economet. 54 (1992), 159–178.

    Google Scholar 

  • Lee, D. and Schmidt, P.: On the power of the KPSS test of stationarity against fractionally-integrated alternatives, J. Economet. 73 (1996), 285–302.

    Google Scholar 

  • Lobato, I and Savin N. E.: Real and spurious long-memory properties of stock market data, J. Business and Eco. Stat. 16 (1998), 261–283.

    Google Scholar 

  • Mandelbrot, B. B.: Statistical methodology for non-periodic cycles: from the covariance to R/S analysis,Ann. Eco. Social Measurement 1 (1972), 259–290.

    Google Scholar 

  • Mandelbrot, B. B.: Limit theorems of the self-normalized range for weakly and strongly dependent processes, Z. Wahrschein. verw. Gebiete 31 (1975), 271–285.

    Google Scholar 

  • Mandelbrot, B. B. and Taqqu, M. S.: Robust R/S analysis of long run serial correlation, in 42nd Session of the International Statistical Institute, Manila, Book 2, 1979, pp. 69–90.

  • Mandelbrot, B. B. and Wallis, J. M.: Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence, Water Resour. Res. 5 (1969), 967–988.

    Google Scholar 

  • Robinson, P. M.: Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression, J. Economet. 47 (1991), 67–84.

    Google Scholar 

  • Robinson, P. M.: Gaussian semiparametric estimation of long range dependence, Ann. Stat. 23 (1995), 1630–1661.

    Google Scholar 

  • Robinson, P. M. and Henry, M.: Bandwidth choice in Gaussian semiparametric estimation of longrange dependence, in P. M. Robinson and M. Rosenblatt (eds), Athens Conference on Applied Probability and Time Series Analysis, vol. II: Time Series Analysis. In memory of E. J. Hannan, Springer-Verlag, New York, 1996, pp. 220–232.

    Google Scholar 

  • Stout, W. F.: Almost Sure Convergence, Academic Press, New York, 1974.

    Google Scholar 

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Giraitis, L., Kokoszka, P., Leipus, R. et al. Semiparametric Estimation of the Intensity of Long Memory in Conditional Heteroskedasticity. Statistical Inference for Stochastic Processes 3, 113–128 (2000). https://doi.org/10.1023/A:1009951213271

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