TESTING FOR THE MARKOV PROPERTY IN TIME SERIES
提出一种基于条件特征函数的频域检验方法，用于检验时间序列是否具有马尔可夫性质，适用于单变量和多变量序列，并通过模拟和金融数据验证了其有效性。
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.