Annals of Statistics

Nonparametric tests of the Markov hypothesis in continuous-time models

Yacine Aït-Sahalia, Jianqing Fan, and Jiancheng Jiang

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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


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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.