Some applications of nonlinear and non-Gaussian state–space modelling by means of hidden Markov models

Roland Langrock

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

Nonlinear and non-Gaussian state–space models (SSMs) are fitted to different types of time series. The applications include homogeneous and seasonal time series, in particular earthquake counts, polio counts, rainfall occurrence data, glacial varve data and daily returns on a share. The considered SSMs comprise Poisson, Bernoulli, gamma and Student-t distributions at the observation level. Parameter estimations for the SSMs are carried out using a likelihood approximation that is obtained after discretization of the state space. The approximation can be made arbitrarily accurate, and the approximated likelihood is precisely that of a finite-state hidden Markov model (HMM). The proposed method enables us to apply standard HMM techniques. It is easy to implement and can be extended to all kinds of SSMs in a straightforward manner.
Original languageEnglish
Pages (from-to)2955-2970
JournalJournal of Applied Statistics
Volume38
Issue number12
Early online date24 Jun 2011
DOIs
Publication statusPublished - 2011

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