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Testing the Markov property with high frequency data. (English) Zbl 1418.62378
Summary: 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.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62G10 Nonparametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
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