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.
Similar content being viewed by others
References
Baillie, R. T., Bollerslev, T. and Mikkelsen, H. O.: Fractionally integrated generalized autoregressive conditional heteroskedasticity, J. Economet. 74 (1996), 3–30.
Beran, J.: Statistics for Long-Memory Processes, Chapman & Hall, New York, 1994.
Campbell, J. Y., Lo, A.W. and MacKinlay, A. C.: The Econometrics of Financial Markets, Princeton University Press, Princeton, 1997.
Delgado, M. A. and Robinson, P. M.: Optimal spectral bandwidth for long memory, Statistica Sinica 6 (1996), 97–112.
Ding, Z. and Granger, C. W. J.: Modeling volatility persistence of speculative returns: a new approach, J. Economet. 73 (1996), 185–215.
Giraitis, L., Kokoszka, P. and Leipus, R.: Stationary ARCH models: dependence structure and Central Limit Theorem, Econometric Theory 16 (2000), 3–22.
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.
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.
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.
Lee, D. and Schmidt, P.: On the power of the KPSS test of stationarity against fractionally-integrated alternatives, J. Economet. 73 (1996), 285–302.
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.
Mandelbrot, B. B.: Statistical methodology for non-periodic cycles: from the covariance to R/S analysis,Ann. Eco. Social Measurement 1 (1972), 259–290.
Mandelbrot, B. B.: Limit theorems of the self-normalized range for weakly and strongly dependent processes, Z. Wahrschein. verw. Gebiete 31 (1975), 271–285.
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.
Robinson, P. M.: Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression, J. Economet. 47 (1991), 67–84.
Robinson, P. M.: Gaussian semiparametric estimation of long range dependence, Ann. Stat. 23 (1995), 1630–1661.
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.
Stout, W. F.: Almost Sure Convergence, Academic Press, New York, 1974.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1023/A:1009951213271