NONPARAMETRIC TESTS OF THE MARKOV HYPOTHESIS IN CONTINUOUS-TIME MODELS

• 成果类型: Article
• 署名作者: Ait-Sahalia, Yacine; Fan, Jianqing; Jiang, Jiancheng
• 署名单位: Princeton University; National Bureau of Economic Research; Princeton University; University of North Carolina; University of North Carolina Charlotte
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS763
• 发表日期: 2010
• 页码: 3129-3163
• 关键词: term structure; interest-rates; conditional densities; specification; regression; bond

摘要

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