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Nonparametric tests of the Markov hypothesis in continuous-time models

Yacine At-Sahalia Jianqing Fan Jiancheng Jiang

Statistics Theory and Methods mathscidoc:1912.43361

The Annals of Statistics, 38, (5), 3129-3163, 2010
We propose several statistics to test the Markov hypothesis for -mixing stationary processes sampled at discrete time intervals. Our tests are based on the ChapmanKolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilkss 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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@inproceedings{yacine2010nonparametric,
  title={Nonparametric tests of the Markov hypothesis in continuous-time models},
  author={Yacine At-Sahalia, Jianqing Fan, and Jiancheng Jiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113934456135921},
  booktitle={The Annals of Statistics},
  volume={38},
  number={5},
  pages={3129-3163},
  year={2010},
}
Yacine At-Sahalia, Jianqing Fan, and Jiancheng Jiang. Nonparametric tests of the Markov hypothesis in continuous-time models. 2010. Vol. 38. In The Annals of Statistics. pp.3129-3163. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113934456135921.
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