Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives
AbstractThe 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1998-142.
Date of creation: 1998
Date of revision:
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Web page: http://center.uvt.nl
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;
Other versions of this item:
- J. Durbin & S. J. Koopman, 2000. "Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-03-08 (All new papers)
- NEP-ECM-1999-03-08 (Econometrics)
- NEP-ETS-1999-03-08 (Econometric Time Series)
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