Asymptotics for Duration-Driven Long Range Dependent Processes

Mengchen Hsieh, Clifford Hurvich and Philippe Soulier
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Mengchen Hsieh: New York University
Clifford Hurvich: New York University
Philippe Soulier: Universite Paris X

Econometrics from University Library of Munich, Germany

Abstract: 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.

Keywords: Long Memory; Structural Change (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2004-12-15
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: Type of Document - pdf; pages: 40
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Related works:
Journal Article: Asymptotics for duration-driven long range dependent processes (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0412009

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