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Semiparametric hidden Markov models: identifiability and estimation

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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
True parameter—contour plot. (a) State 1 and (b) State 2.
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(a) Series of log‐returns of the two stocks. (b) Global decoding using the Viterbi‐algorithm based on parameter estimates from parametric fit (a) and nonparametric log‐concave fit (b).
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Log‐concave estimation. (a) State 1, (b) State 2, and (c) State 3.
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Log‐concave estimation.
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Parametric estimation.
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Log‐concave estimation—contour plot. (a) State 1 and (b) State 2.
[ Normal View | Magnified View ]

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Statistical Models > Model Selection
Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
Statistical and Graphical Methods of Data Analysis > EM Algorithm
Applications of Computational Statistics > Computational Finance

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