Statistical inference for the nonparametric and semiparametric hidden Markov model via the composite likelihood approach  

作　　者：Mian Huang Yue Huang Weixin Yao 

机构地区：[1]School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai 200433,China [2]Department of Statistics,University of California,Riverside,Riverside,CA 92521,USA

出　　处：《Science China Mathematics》2023年第3期601-626,共26页中国科学：数学（英文版）

基　　金：supported by Shanghai Young Talent Development Program and Innovative Research Team of Shanghai University of Finance and Economics(Grant No.2020110930);supported by the Department of Energy of USA(Grant No.DE-EE0008574)。

摘　　要：In this paper, we propose a new estimation method for a nonparametric hidden Markov model(HMM), in which both the emission model and the transition matrix are nonparametric, and a semiparametric HMM, in which the transition matrix is parametric while emission models are nonparametric. The estimation is based on a novel composite likelihood method, where the pairs of consecutive observations are treated as independent bivariate random variables. Therefore, the model is transformed into a mixture model, and a modified expectation-maximization(EM) algorithm is developed to compute the maximum composite likelihood.We systematically study asymptotic properties for both the nonparametric HMM and the semiparametric HMM. We also propose a generalized likelihood ratio test to choose between the nonparametric HMM and the semiparametric HMM. We derive the asymptotic distribution and prove the Wilk’s phenomenon of the proposed test statistics. Simulation studies and an application in volatility clustering analysis of the volatility index in the Chicago Board Options Exchange(CBOE) are conducted to demonstrate the effectiveness of the proposed methods.

关 键 词：nonparametric HMM nonhomogeneous HMM semiparametric estimate composite likelihood generalized likelihood ratio test 

分 类 号：O211.6[理学—概率论与数理统计]