Journal
JOURNAL OF APPLIED STATISTICS
Volume 38, Issue 12, Pages 2955-2970Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02664763.2011.573543
Keywords
time series; numerical integration; count data; binary data; stochastic volatility; pseudo-residuals; Viterbi algorithm
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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.
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