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Testing The Markov Property with Ultra High Frequency Financial Data

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  • Matos, João Manuel Gonçalves 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 FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 414.

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Date of creation: 01 Mar 2001
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Handle: RePEc:fgv:epgewp:414

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  1. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  2. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  3. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation for Research in Economics, Yale University.
  4. David Easley & Soeren Hvidkjaer & Maureen O'Hara, 2002. "Is Information Risk a Determinant of Asset Returns?," Journal of Finance, American Finance Association, vol. 57(5), pages 2185-2221, October.
  5. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, 07.
  6. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  7. Easley, David & O'Hara, Maureen, 1992. " Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
  8. 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 wp389, Universidade Nova de Lisboa, Faculdade de Economia.
  9. Marcelo Fernandes & Joachim Grammig, 2000. "Non-Parametric Specification Tests For Conditional Duration Models," Computing in Economics and Finance 2000 40, Society for Computational Economics.
  10. E, Burgayran & Serge Darolles, 1997. "Nonparametric Estimation of a Diffusion Equation from Tick Observations," Working Papers 97-56, Centre de Recherche en Economie et Statistique.
  11. Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers 1140, Cowles Foundation for Research in Economics, Yale University.
  12. Easley, David & Kiefer, Nicholas M & O'Hara, Maureen, 1997. "One Day in the Life of a Very Common Stock," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 805-35.
  13. Easley, David & O'Hara, Maureen, 1987. "Price, trade size, and information in securities markets," Journal of Financial Economics, Elsevier, vol. 19(1), pages 69-90, September.
  14. Su, Liangjun & White, Halbert, 2003. "A Consistent Characteristic-Function-Based Test for Conditional Independence," University of California at San Diego, Economics Working Paper Series qt4dv0837f, Department of Economics, UC San Diego.
  15. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
  16. repec:fth:inseep:9756 is not listed on IDEAS
  17. GIOT, Pierre, 1999. "Time transformations, intraday data and volatility models," CORE Discussion Papers 1999044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
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