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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. Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1148, Cowles Foundation for Research in Economics, Yale University.
  2. Fernandes, Marcelo & Grammig, Joachim, 2003. "Nonparametric specification tests for conditional duration models," Economics Working Papers (Ensaios Economicos da EPGE) 502, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  3. repec:fth:inseep:9756 is not listed on IDEAS
  4. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 807-834, December.
  5. E, Burgayran & Serge Darolles, 1997. "Nonparametric Estimation of a Diffusion Equation from Tick Observations," Working Papers, Centre de Recherche en Economie et Statistique 97-56, Centre de Recherche en Economie et Statistique.
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  8. Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1140, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
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  14. Easley, David & O'Hara, Maureen, 1987. "Price, trade size, and information in securities markets," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(1), pages 69-90, September.
  15. David Easley & Soeren Hvidkjaer & Maureen O'Hara, 2002. "Is Information Risk a Determinant of Asset Returns?," Journal of Finance, American Finance Association, American Finance Association, vol. 57(5), pages 2185-2221, October.
  16. Robinson, P M, 1991. "Consistent Nonparametric Entropy-Based Testing," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 58(3), pages 437-53, May.
  17. 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, Elsevier, vol. 14(1), pages 71-100, March.
  18. GIOT, Pierre, 1999. "Time transformations, intraday data and volatility models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1999044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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