Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives

J. Durbin, S.J.M. Koopman

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Abstract

The analysis of non-Gaussian time series using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Monte Carlo Markov chain methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state vector given the observations, and the mean square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution functions. Choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally effcient. Their use is illustrated by applying to a univariate discrete time series, a series with outliers and a volatility series.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages26
Volume1998-142
Publication statusPublished - 1998

Publication series

NameCentER Discussion Paper
Volume1998-142

Keywords

  • Antithetic variables
  • Conditional and posterior statistics
  • Exponential family distributions
  • Heavy-tailed distributions
  • Importance sampling
  • Kalman filtering and smoothing
  • Monte Carlo simulation
  • Non-Gaussian time series models
  • Posterior distributions

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