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A note on the mixture transition distribution and hidden Markov models
Author(s) -
Bartolucci Francesco,
Farcomeni Alessio
Publication year - 2010
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2009.00650.x
Subject(s) - hidden markov model , mathematics , hidden semi markov model , markov chain , markov model , latent variable , variable order markov model , markov property , interpretation (philosophy) , econometrics , maximum entropy markov model , series (stratigraphy) , algorithm , statistics , artificial intelligence , computer science , programming language , paleontology , biology
We discuss an interpretation of the mixture transition distribution (MTD) for discrete‐valued time series which is based on a sequence of independent latent variables which are occasion‐specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the hidden Markov model (HMM). For these models we outline an EM algorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. As an illustration, we provide an example based on the analysis of stock market data referred to different American countries.