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Semiparametric hidden Markov models: identifiability and estimation
Author(s) -
Dannemann Jörn,
Holzmann Hajo,
Leister Anna
Publication year - 2014
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.1326
Subject(s) - identifiability , hidden markov model , computer science , nonparametric statistics , parametric statistics , graphical model , statistical model , markov chain , algorithm , bivariate analysis , markov model , mathematics , artificial intelligence , econometrics , machine learning , statistics
We review the theory on semiparametric hidden Markov models ( HMMs ), that is, HMMs for which the state‐dependent distributions are not fully parametrically, but rather semi‐ or nonparametrically specified. We start by reviewing identifiability in such models, where by exploiting the dependence much stronger results can be achieved than for independent finite mixtures. We also discuss estimation, in particular in an algorithmic fashion by using appropriate versions or modifications of the Baum‐Welch (or EM ) algorithm. We present some simulation results and give an application to modeling bivariate financial time series, where we compare parametric with nonparametric fits for the state‐dependent distributions as well as the resulting state‐decoding. WIREs Comput Stat 2014, 6:418–425. doi: 10.1002/wics.1326 This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > EM Algorithm Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical Models > Model Selection