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TESTING FOR THE MARKOV PROPERTY IN TIMESERIES

Published online by Cambridge University Press:  07 June 2011

Bin Chen and
Yongmiao Hong
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Abstract

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The Markov property is a fundamental property in timeseries analysis and is often assumed in economic andfinancial modeling. We develop a new test for theMarkov property using the conditional characteristicfunction embedded in a frequency domain approach,which checks the implication of the Markov propertyin every conditional moment (if it exists) and overmany lags. The proposed test is applicable to bothunivariate and multivariate time series withdiscrete or continuous distributions. Simulationstudies show that with the use of a smoothednonparametric transition density-based bootstrapprocedure, the proposed test has reasonable sizesand all-around power against several popularnon-Markov alternatives in finite samples. We applythe test to a number of financial time series andfind some evidence against the Markov property.

Information

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 1 , February 2012, pp. 130 - 178
Copyright
Copyright © Cambridge University Press 2011

Footnotes

We thank Pentti Saikkonen (the co-editor), threereferees, Frank Diebold, Oliver Linton, JamesMacKinnon, Katsumi Shimotsu, Kyungchul Song,Liangjun Su, George Tauchen, and seminarparticipants at Peking University, Queen’sUniversity, University of Pennsylvania, the 2008Xiamen University-Humboldt University JointWorkshop, the 2008 International Symposium onRecent Developments of Time Series Econometrics inXiamen, the 2008 Symposium on Econometric Theoryand Applications (SETA) in Seoul, and the 2008 FarEastern Econometric Society Meeting in Singaporefor their constructive comments on the previousversions of this paper. Any remaining errors aresolely ours. Bin Chen thanks the Department ofEconomics, University of Rochester, for financialsupport. Yongmiao Hong thanks the outstandingoverseas youth fund of the National ScienceFoundation of China for its support.

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