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http://ssrn.com/abstract=1293612
 
 

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Asymptotics for Duration-Driven Long Range Dependent Processes


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

August 2003

NYU Working Paper No. SOR-2003-8

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.

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Date posted: November 3, 2008  

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: http://ssrn.com/abstract=1293612

Contact Information

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
Feedback to SSRN


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