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TESTING FOR THE MARKOV PROPERTY IN TIME SERIES

Published online by Cambridge University Press:  07 June 2011

Abstract

The Markov property is a fundamental property in time series analysis and is often assumed in economic and financial modeling. We develop a new test for the Markov property using the conditional characteristic function embedded in a frequency domain approach, which checks the implication of the Markov property in every conditional moment (if it exists) and over many lags. The proposed test is applicable to both univariate and multivariate time series with discrete or continuous distributions. Simulation studies show that with the use of a smoothed nonparametric transition density-based bootstrap procedure, the proposed test has reasonable sizes and all-around power against several popular non-Markov alternatives in finite samples. We apply the test to a number of financial time series and find some evidence against the Markov property.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

We thank Pentti Saikkonen (the co-editor), three referees, Frank Diebold, Oliver Linton, James MacKinnon, Katsumi Shimotsu, Kyungchul Song, Liangjun Su, George Tauchen, and seminar participants at Peking University, Queen’s University, University of Pennsylvania, the 2008 Xiamen University-Humboldt University Joint Workshop, the 2008 International Symposium on Recent Developments of Time Series Econometrics in Xiamen, the 2008 Symposium on Econometric Theory and Applications (SETA) in Seoul, and the 2008 Far Eastern Econometric Society Meeting in Singapore for their constructive comments on the previous versions of this paper. Any remaining errors are solely ours. Bin Chen thanks the Department of Economics, University of Rochester, for financial support. Yongmiao Hong thanks the outstanding overseas youth fund of the National Science Foundation of China for its support.

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