Asymptotics for Duration-Driven Long Range Dependent Processes
We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration- driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an $iid$ process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized autocovariances at fixed lags. Finite collections of standardized autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ghysels, E. & Harvey, A. & Renault, E., 1996.
Cahiers de recherche
9613, Universite de Montreal, Departement de sciences economiques.
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
- Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Velasco, Carlos, 1998.
"Non-Gaussian log-periodogram regression,"
DES - Working Papers. Statistics and Econometrics. WS
4553, Universidad Carlos III de Madrid. Departamento de Estadística.
- Terrin, Norma & Hurvich, Clifford M., 1994. "An asymptotic Wiener-Itô representation for the low frequency ordinates of the periodogram of a long memory time series," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 297-307, December.
- Rohit Deo & Meng-Chen Hsieh & Clifford M. Hurvich & Philippe Soulier, 2007. "Long Memory in Nonlinear Processes," Papers 0706.1836, arXiv.org.
- William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
- Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
- Hurvich, Clifford M. & Soulier, Philippe, 2002. "Testing For Long Memory In Volatility," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1291-1308, December.
- Tieslau, Margie A. & Schmidt, Peter & Baillie, Richard T., 1996. "A minimum distance estimator for long-memory processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 249-264.
- Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
- Hurvich, Clifford M. & Moulines, Eric & Soulier, Philippe, 2002. "The FEXP estimator for potentially non-stationary linear time series," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 307-340, February.
- Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, vol. 117(1), pages 95-121, November.
- Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
- Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(01), pages 51-78, February.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:0412009. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.