Nonparametric tests of the Markov hypothesis in continuous-time models

Details Nonparametric tests of the Markov hypothesis in continuous-time models Nonparametric tests of the Markov hypothesis in continuous-time models

2010-11-11

arxiv.org/abs/1011.2645v1

Annals of Statistics 2010, Vol. 38, No. 5, 3129-3163

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS763 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS763

We propose several statistics to test the Markov hypothesis for $\beta$-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman--Kolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilks's phenomenon holds. We compute the power of the test and provide simulations to investigate the finite sample performance of the 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.

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