Limit Laws in Transaction-Level Asset Price Models

49 Pages Posted: 21 Jul 2012

See all articles by Alexander Aue

Alexander Aue

University of California, Davis

Lajos Horváth

University of Utah - Department of Mathematics

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

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Date Written: July 2012

Abstract

We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal patterns in volatility, and non-trading periods that may be different for the two assets. We also allow for asymmetries (leverage effects). We obtain the asymptotic distribution of the log-price process. For the weak fractional cointegration case, we obtain the asymptotic distribution of the ordinary least-squares estimator of the cointegrating parameter based on data sampled from an equally-spaced discretization of calendar time, and justify a feasible method of hypothesis testing for the cointegrating parameter based on the corresponding t-statistic. In the strong fractional cointegration case, we obtain the limiting distribution of a continuously-averaged tapered estimator as well as other estimators of the cointegrating parameter, and find that the rate of convergence can be affected by properties of intertrade durations. In particular, the persistence of durations (hence of volatility) can affect the degree of cointegration. We also obtain the rate of convergence of several estimators of the cointegrating parameter in the standard cointegration case. Finally, we consider the properties of the ordinary least squares estimator of the regression parameter in a spurious regression, i.e., in the absence of cointegration.

Suggested Citation

Aue, Alexander and Horváth, Lajos and Hurvich, Clifford M. and Soulier, Philippe, Limit Laws in Transaction-Level Asset Price Models (July 2012). NYU Working Paper No. SOR-2012-02. Available at SSRN: https://ssrn.com/abstract=2114875

Alexander Aue

University of California, Davis ( email )

One Shields Avenue
Davis, CA 95616
United States

Lajos Horváth

University of Utah - Department of Mathematics ( email )

1645 E. Campus Center
Salt Lake City, UT 84112
United States
801 581-8159 (Phone)

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)

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