Summary: The Annals of Statistics
2010, Vol. 38, No. 5, 3129­3163
DOI: 10.1214/09-AOS763
© Institute of Mathematical Statistics, 2010
NONPARAMETRIC TESTS OF THE MARKOV HYPOTHESIS IN
CONTINUOUS-TIME MODELS1
BY YACINE AÏT-SAHALIA, JIANQING FAN AND JIANCHENG JIANG
Princeton University and NBER, Princeton University and University of
North Carolina at Charlotte
We propose several statistics to test the Markov hypothesis for -mixing
stationary processes sampled at discrete time intervals. Our tests are based on
the Chapman­Kolmogorov equation. We establish the asymptotic null dis-
tributions of the proposed test statistics, showing that Wilks's phenomenon
holds. We compute the power of the test and provide simulations to investi-
gate 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.
1. Introduction. Among stochastic processes, those that satisfy the Markov
property represent an important special case. The Markov property restricts the
effective size of the filtration that governs the dynamics of the process. In a nut-

Source: Aït-Sahalia, Yacine - Program in Applied and Comptutational Mathematics & Department of Economics, Princeton University
Fan, Jianqing - Department of Operations Research and Financial Engineering, Princeton University
Jiang, Jiancheng - Department of Mathematics and Statistics, University of North Carolina at Charlotte

Collections: Mathematics