Propagation of Memory Parameter from Durations to Counts

28 Pages Posted: 3 Nov 2008

See all articles by Rohit Deo

Rohit Deo

Stern School of Business, New York University

Clifford M. Hurvich

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

Philippe Soulier

Université d'Évry

Yi Wang

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

Date Written: November 2005

Abstract

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter d 2 [0; 1=2) to ensure that the corresponding counting process N(t) satisfies VarN(t) » Ct2d+1 (C > 0) as t ! 1, with the same memory parameter d 2 [0; 1=2) that was assumed for the durations. Thus, these conditions ensure that the memory in durations propagates to the same memory parameter in counts and therefore in realized volatility. We then show that any Autoregressive Conditional Duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, while any Long Memory Stochastic Duration model with d > 0 and all finite moments yields long memory in counts, with the same d. Finally, we present a result implying that the onlyway for a series of counts aggregated over a long time period to have nontrivial autocorrelation is for the short-term counts to have long memory. In other words, aggregation ultimately destroys allautocorrelation in counts, if and only if the counts have short memory.

Keywords: Long Memory Stochastic Duration, Autoregressive Conditional Duration, Rosenthal type Inequality

Suggested Citation

Deo, Rohit and Hurvich, Clifford M. and Soulier, Philippe and Wang, Yi, Propagation of Memory Parameter from Durations to Counts (November 2005). Statistics Working Papers Series, Vol. , pp. -, 2005. Available at SSRN: https://ssrn.com/abstract=1293161

Rohit Deo

Stern School of Business, New York University ( email )

44 West Fourth Street
New York, NY 10012
United States

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 Soulier

Université d'Évry ( email )

F-91025 Evry Cedex
France
33 (0)1 69 47 02 28 (Phone)
33 (0)1 69 47 02 18 (Fax)

Yi Wang

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

44 West Fourth Street
New York, NY 10012
United States

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