Asymptotics for Duration-Driven Long Range Dependent Processes

40 Pages Posted: 3 Nov 2008

See all articles by Mengchen Hsieh

Mengchen Hsieh

affiliation not provided to SSRN

Clifford M. Hurvich

Stern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences

Philippe Souliery

affiliation not provided to SSRN

Date Written: August 2003

Abstract

We consider processes with second order long range dependence resulting from heavytailed 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 onfractional di erencing of an iid process. We consider in detail two speci c processes hav-ing DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For theseprocesses, we obtain the limiting distribution of suitably standardized discrete Fourier trans forms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized autocovariances at xed lags. Finite collections of standardized autocovariances at a xed 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 calibrateour asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter.

Suggested Citation

Hsieh, Mengchen and Hurvich, Clifford M. and Souliery, Philippe, Asymptotics for Duration-Driven Long Range Dependent Processes (August 2003). Statistics Working Papers Series, Vol. , pp. -, 2003. Available at SSRN: https://ssrn.com/abstract=1293612

Mengchen Hsieh

affiliation not provided to SSRN ( email )

Clifford M. Hurvich

Stern School of Business, New York University ( email )

44 West 4th Street
New York, NY 10012-1126
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

Philippe Souliery

affiliation not provided to SSRN

No Address Available

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