Semiparametric hidden Markov models: identifiability and estimation
Jörn Dannemann, Hajo Holzmann, Anna Leister · Wiley Interdisciplinary Reviews Computational Statistics · 2014
We review the theory on semiparametric hidden Markov models (HMMs), that is,HMMsfor 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 (orEM) 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 Stat2014, 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