Purpose:To propose a few statistics to test the Markov hypothesis for -mixing stationary process sampled at discrete time intervals.Summary:The proposed tests are based on the Chapman-Kolmogorov (CK) equation. Asymptotic null distributions of the proposed test statistics are established showing that Wilk's phenomenon holds. The power of the test is computed and simulations are provided to investigate finite sample performance of test statistics when the null model is a diffusion process, with alternatives consisting of models with a stochastic mean reversion level, stochastic volatility and jumps. (30 refs.)
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