TESTING THE MARKOV PROPERTY WITH ULTRA HIGH FREQUENCY FINANCIAL DATA.pdf

TESTING THE MARKOV PROPERTY WITH ULTRA HIGH FREQUENCY FINANCIAL DATA? Joa?o Amaro de Matos Marcelo Fernandes Faculdade de Economia Graduate School of Economics Universidade Nova de Lisboa Fundac?a?o Getulio Vargas Rua Marque?s de Fronteira, 20 Praia de Botafogo, 190 1099-038 Lisbon, Portugal 22953-900 Rio de Janeiro, Brazil Tel: +351.21.3826100 Tel: +55.21.5595827 Fax: +351.21.3873973 Fax: +55.21.5538821 amatos@fe.unl.pt mfernand@fgv.br March 2001 ? The second author gratefully acknowledges the hospitality of the Univer- sidade Nova de Lisboa, where part of this paper was written, and a Jean Monnet fellowship at the European University Institute. 1 TESTING THE MARKOV PROPERTY WITH ULTRA HIGH FREQUENCY FINANCIAL DATA Abstract: This paper develops a framework to test whether discrete-valued irregularly-spaced financial transactions data follow a subordinated 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 not only the irregular spacing of transactions data, but also price discreteness. Further, it turns out that, under such an observation rule, the current price duration is independent of previous price durations given the current price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Finally, we investigate whether or not 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. The results are mixed in the sense that the Markov assumption is rejected for three out of the five stocks we have analyzed. JEL Classification: C14, C52, G10, G19. Keywords: Bid-ask spread, nonparametric tests, price durations, subordi- nated Markov pr