Open Access
October 2010 Nonparametric tests of the Markov hypothesis in continuous-time models
Yacine Aït-Sahalia, Jianqing Fan, Jiancheng Jiang
Ann. Statist. 38(5): 3129-3163 (October 2010). DOI: 10.1214/09-AOS763


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.


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Yacine Aït-Sahalia. Jianqing Fan. Jiancheng Jiang. "Nonparametric tests of the Markov hypothesis in continuous-time models." Ann. Statist. 38 (5) 3129 - 3163, October 2010.


Published: October 2010
First available in Project Euclid: 13 September 2010

zbMATH: 1200.62066
MathSciNet: MR2722466
Digital Object Identifier: 10.1214/09-AOS763

Primary: 60J60 , 62G10
Secondary: 62G20

Keywords: Chapman–Kolmogorov equation , diffusion , locally linear smoother , Markov hypothesis , Transition density

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 5 • October 2010
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