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Testing the Markov property with ultra-high frequency financial data

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  • Matos, Joao Amaro de
  • Fernandes, Marcelo

Abstract

This paper develops a framework to nonparametrically test whether discretevalued 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 not only the irregular spacing of transactions data, but also price discreteness. 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.

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Bibliographic Info

Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp462.

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Length: 25 pages
Date of creation: 2004
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Handle: RePEc:unl:unlfep:wp462

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Keywords: Bid-ask spread; nonparametric testing; price durations; Markov property; ultra-high frequency data;

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  1. Su, Liangjun & White, Halbert, 2003. "A Consistent Characteristic-Function-Based Test for Conditional Independence," University of California at San Diego, Economics Working Paper Series, Department of Economics, UC San Diego qt4dv0837f, Department of Economics, UC San Diego.
  2. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, Elsevier, vol. 127(1), pages 35-68, July.
  3. Matos, Joao Amaro de & Rosario, Joao Sobral do, 2000. "The Equilibrium Dynamics for an Endogeneous Bid-Ask Spread in a Monopolistic financial Market," FEUNL Working Paper Series, Universidade Nova de Lisboa, Faculdade de Economia wp389, Universidade Nova de Lisboa, Faculdade de Economia.
  4. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
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