Nonparametric tests of the Markov hypothesis in continuous-time models

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Abstract

We propose several statistics to test the Markov hypothesis for β-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.

Original languageEnglish (US)
Pages (from-to)3129-3163
Number of pages35
JournalAnnals of Statistics
Volume38
Issue number5
DOIs
StatePublished - Oct 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Chapman-Kolmogorov equation
  • Diffusion.
  • Locally linear smoother
  • Markov hypothesis
  • Transition density

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