Hurvich, Cliiford and Wang, Yi (2006): A PureJump TransactionLevel Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects.

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Abstract
We propose a new transactionlevel bivariate logprice model, which yields fractional or standard cointegration. To the best of our knowledge, all existing models for cointegration require the choice of a fixed sampling frequency Delta t. By contrast, our proposed model is constructed at the transaction level, thus determining the properties of returns at all sampling frequencies. The two ingredients of our model are a Long Memory Stochastic Duration process for the waiting times tau(k) between trades, and a pair of stationary noise processes ( e(k) and eta(k) ) which determine the jump sizes in the purejump logprice process. The e(k), assumed to be iid Gaussian, produce a Martingale component in log prices. We assume that the microstructure noise eta(k) obeys a certain model with memory parameter d(eta) in (1/2,0) (fractional cointegration case) or d(eta) = 1 (standard cointegration case). Our logprice model includes feedback between the shocks of the two series. This feedback yields cointegration, in that there exists a linear combination of the two components that reduces the memory parameter from 1 to 1+d(eta) in (0.5,1) and (0). Returns at sampling frequency Delta t are asymptotically uncorrelated at any fixed lag as Delta t increases. We prove that the cointegrating parameter can be consistently estimated by the ordinary leastsquares estimator, and obtain a lower bound on the rate of convergence. We propose transactionlevel methodofmoments estimators of several of the other parameters in our model. We present a data analysis, which provides evidence of fractional cointegration. We then consider special cases and generalizations of our model, mostly in simulation studies, to argue that the suitablymodified model is able to capture a variety of additional properties and stylized facts, including leverage, portfolio return autocorrelation due to nonsynchronous trading, Granger causality, and volatility feedback. The ability of the model to capture these effects stems in most cases from the fact that the model treats the (stochastic) intertrade durations in a fully endogenous way.
Item Type:  MPRA Paper 

Institution:  Stern, NYU 
Original Title:  A PureJump TransactionLevel Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects 
Language:  English 
Keywords:  Tick Time; Long Memory Stochastic Duration; Information Share; Granger causality 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C00  General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  1413 
Depositing User:  Yi Wang 
Date Deposited:  11. Jan 2007 
Last Modified:  21. Feb 2013 10:39 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/1413 