Nonparametric tests of the Markov hypothesis in continuous-time models
Abstract
We propose several statistics to test the Markov hypothesis for -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.
Cite
@article{arxiv.1011.2645,
title = {Nonparametric tests of the Markov hypothesis in continuous-time models},
author = {Yacine Aït-Sahalia and Jianqing Fan and Jiancheng Jiang},
journal= {arXiv preprint arXiv:1011.2645},
year = {2016}
}
Comments
Published in at http://dx.doi.org/10.1214/09-AOS763 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)