Limit Laws in Transaction-Level Asset Price Models

22 Pages Posted: 8 Jun 2009

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

Date Written: May 2009

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. Most assumptions are stated directly on the point process, though we provide sufficient conditions on the corresponding inter-trade durations for these assumptions to hold. We obtain the asymptotic distribution of the log-price process. We also 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, in the case of weak fractional cointegration. Finally, we obtain the limiting distribution of the ordinary least-squares estimator of the autoregressive parameter in a simplified transaction-level univariate model with a unit root.

Suggested Citation

Aue, Alexander and Horváth, Lajos and Hurvich, Clifford M., Limit Laws in Transaction-Level Asset Price Models (May 2009). Statistics Working Papers Series, Vol. , pp. -, 2009. Available at SSRN: https://ssrn.com/abstract=1415225

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

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