Annals of Statistics
- Ann. Statist.
- Volume 38, Number 5 (2010), 3129-3163.
Nonparametric tests of the Markov hypothesis in continuous-time models
Yacine Aït-Sahalia, Jianqing Fan, and Jiancheng Jiang
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.
Article information
Source
Ann. Statist., Volume 38, Number 5 (2010), 3129-3163.
Dates
First available in Project Euclid: 13 September 2010
Permanent link to this document
https://projecteuclid.org/euclid.aos/1284391760
Digital Object Identifier
doi:10.1214/09-AOS763
Mathematical Reviews number (MathSciNet)
MR2722466
Zentralblatt MATH identifier
1200.62066
Subjects
Primary: 62G10: Hypothesis testing 60J60: Diffusion processes [See also 58J65]
Secondary: 62G20: Asymptotic properties
Keywords
Markov hypothesis Chapman–Kolmogorov equation locally linear smoother transition density diffusion
Citation
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
Supplemental materials
- 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.Digital Object Identifier: doi:10.1214/09-AOS763SUPP