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LIMIT LAWS IN TRANSACTION-LEVEL ASSET PRICE MODELS

Published online by Cambridge University Press:  18 November 2013

Alexander Aue ,
Lajos Horváth ,
Clifford Hurvich  and
Philippe Soulier
Alexander Aue
Affiliation:
University of California, Davis
Lajos Horváth
Affiliation:
University of Utah
Clifford Hurvich*
Affiliation:
New York University
Philippe Soulier
Affiliation:
Université Paris X
*
*Address correspondence to Clifford Hurvich, Stern School of Business, New York University, 44 West 4th Street, New York NY 10012 USA. e-mail: churvich@stern.nyu.edu
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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 nontrading 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 we 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 we 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.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 3 , June 2014 , pp. 536 - 579
Copyright
Copyright © Cambridge University Press 2013 

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