Nonparametric tests of the Markov hypothesis in continuous-time models
Yacine Aït-Sahalia, Jianqing Fan, Jiancheng Jiang
The Annals of Statistics · 2010 · Volume 38 · Issue 5
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.
Keywords
60J60, 62G10, 62G20, Chapman–Kolmogorov equation, diffusion, locally linear smoother, Markov hypothesis, Transition density
Enable JavaScript for citation tools and additional paper interactions.