Testing the Markov property with high frequency data

• Published in: Journal of econometrics 2007-11, Vol.141 (1), p.44-64
• Main Authors: Amaro de Matos, João, Fernandes, Marcelo
• Format: Article
• Language: English
• Subjects: Applications; Asymptotic methods; Bid–ask spread; Capital market; Conditional independence; Duration; Econometrics; Exact sciences and technology; Global analysis, analysis on manifolds; Inference from stochastic processes; time series analysis; Insurance, economics, finance; Markov analysis; Markov processes; Mathematics; Modelling; Monte Carlo simulation; Nonparametric testing; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Spread; Statistical methods; Statistics; Studies; Testing; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; U-statistic
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2007.01.007

This paper develops a framework to nonparametrically test whether discrete-valued irregularly spaced financial transactions data follow a Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates the irregular spacing that characterizes transactions data. Under such an observation rule, the current price duration is independent of a previous price duration given the previous price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Monte Carlo simulations suggest that the asymptotic test has huge size distortions, though a bootstrap-based variant entails reasonable size and power properties in finite samples. As for an empirical illustration, we investigate whether bid–ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid–ask spread. We robustly reject the Markov assumption for two out of the five stocks under scrutiny. Finally, it is reassuring that our results are consistent with two alternative measures of asymmetric information.