Estimation and testing of nonparametric hidden Markov model with application in stock market

Abstract

In this paper, a fully nonparametric Hidden Markov Model is proposed, where both the state dependent emission model and transition matrix are all nonparametric and depend on a covariate. By reducing modeling bias, the new model extends the applicability of both the semiparametric HMM with nonparametric emission model and nonhomogeneous HMM. A modified EM algorithm, which combines the kernel regression technique, is proposed for estimation. Model selection procedures are provided and a conditional bootstrap method is employed to assess the standard errors of the estimates. A generalized likelihood ratio test procedure is further proposed and the Wilk’s type of phenomenon is verified to hold for the proposed model. Simulation studies are conducted to demonstrate proposed procedure, and the proposed model is applied in analyzing the impact of economic on stock market.