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

J. Durbin, S.J.M. Koopman

Research output: Working paperDiscussion paperOther research output

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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

Fingerprint

Time Series Analysis
State-space Model
Importance Sampling
Series
Posterior Mean
Markov Chain Monte Carlo Methods
Time Series Models
State Equation
Mean square error
Density Function
Volatility
Outlier
Univariate
Distribution Function
Discrete-time
Disturbance
Cover
Estimate
Observation
Simulation

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

Cite this

Durbin, J., & Koopman, S. J. M. (1998). Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives. (CentER Discussion Paper; Vol. 1998-142). Tilburg: Econometrics.
Durbin, J. ; Koopman, S.J.M. / Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives. Tilburg : Econometrics, 1998. (CentER Discussion Paper).
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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.",
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Durbin, J & Koopman, SJM 1998 'Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives' CentER Discussion Paper, vol. 1998-142, Econometrics, Tilburg.

Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives. / Durbin, J.; Koopman, S.J.M.

Tilburg : Econometrics, 1998. (CentER Discussion Paper; Vol. 1998-142).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

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AB - 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.

KW - Antithetic variables

KW - Conditional and posterior statistics

KW - Exponential family distributions

KW - Heavy-tailed distributions

KW - Importance sampling

KW - Kalman filtering and smoothing

KW - Monte Carlo simulation

KW - Non-Gaussian time series models

KW - Posterior distributions

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

PB - Econometrics

CY - Tilburg

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