Annals of Statistics
- Ann. Statist.
- Volume 38, Number 5 (2010), 3129-3163.
Nonparametric tests of the Markov hypothesis in continuous-time models
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.
Ann. Statist., Volume 38, Number 5 (2010), 3129-3163.
First available in Project Euclid: 13 September 2010
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Aït-Sahalia, Yacine; Fan, Jianqing; Jiang, Jiancheng. Nonparametric tests of the Markov hypothesis in continuous-time models. Ann. Statist. 38 (2010), no. 5, 3129--3163. doi:10.1214/09-AOS763. https://projecteuclid.org/euclid.aos/1284391760
- Supplementary material: Additional technical details. We provide detailed proofs for Lemmas 1–7 and Theorems 5–6. Modern nonparametric smoothing techniques and theory of U-statistics are used.