### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 26 |

Volume | 1998-142 |

Publication status | Published - 1998 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 1998-142 |

### Fingerprint

### 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

*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.

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

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives

AU - Durbin, J.

AU - Koopman, S.J.M.

N1 - Pagination: 26

PY - 1998

Y1 - 1998

N2 - 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.

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

M3 - Discussion paper

VL - 1998-142

T3 - CentER Discussion Paper

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

PB - Econometrics

CY - Tilburg

ER -