Conditions for the Propagation of Memory Parameter from Durations to Counts and Realized Volatility

40 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: June 2009

Abstract

We establish sufficient conditions on durations that arestationary with finite variance and memory parameter $d \in[0,1/2)$ to ensure that the corresponding counting process $N(t)$satisfies $Var N(t) \sim C t^{2d+1}$ ($C>0$) as $t\rightarrow \infty$, with the same memory parameter $d \in[0,1/2)$ that was assumed for the durations. Thus, theseconditions ensure that the memory parameter in durationspropagates to the same memory parameter in the counts. We thenshow that any Autoregressive Conditional Duration ACD(1,1) modelwith a sufficient number of finite moments yields short memory incounts, 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 provide some results about the propagation oflong memory to the empirically-relevant case of realized varianceestimates affected by market microstructure noise contamination.

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, Conditions for the Propagation of Memory Parameter from Durations to Counts and Realized Volatility (June 2009). New York University, Stern School of Business, CeDER, Universite Paris X, Vol. , pp. -, 2009. Available at SSRN: https://ssrn.com/abstract=1293146

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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