Testing for the Markov Property in Time Series

The Markov property is a fundamental property in time series analysis and is often assumed in economic and financial modelling. We develop a 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 exist) 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 non-Markov alternatives in finite samples. We apply the test to a number of high-frequency financial time series and find strong evidence against the Markov property.