A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects

84 Pages Posted: 3 Nov 2008 Last revised: 6 Jun 2009

See all articles by Clifford M. Hurvich

Clifford M. Hurvich

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

Yi Wang

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

Date Written: January 2009

Abstract

We propose a new transaction-level bivariate log-price model, which yields fractional or standard cointegration. The model provides a link between market microstructure and lower-frequency observations. The two ingredients of our model are a Long Memory Stochastic Duration process for thewaiting times between trades, and a pair of stationary noise processes which determine the jump sizes in the pure-jump log-price process. Our model includes feedback between the disturbances of the two log-price series at the transaction level, which induces standard or fractionalcointegration for any fixed sampling interval. We prove that the cointegrating parameter can beconsistently estimated by the ordinary least-squares estimator, and obtain a lower bound on the rate of convergence. We propose transaction-level method-of-moments estimators of the other parameters in our model and discuss the consistency of these estimators. We then use simulations to argue that suitably-modified versions of our model are able to capture a variety of additional properties and stylized facts, including leverage, and portfolio return autocorrelation due to nonsynchronous trading. The ability of the model to capture these effects stems in most cases from the fact that themodel treats the (stochastic) intertrade durations in a fully endogenous way.

Keywords: Tick Time, Long Memory stochastic duration, Information share

Suggested Citation

Hurvich, Clifford M. and Wang, Yi, A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects (January 2009). Statistics Working Papers Series, Vol. , pp. -, 2009. Available at SSRN: https://ssrn.com/abstract=1293153

Clifford M. Hurvich (Contact Author)

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

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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