Bayesian inference and prediction for mean and variance shifts in autoregressive time series

Robert E. McCulloch; Ruey S. Tsay

doi:10.1080/01621459.1993.10476364

Bayesian inference and prediction for mean and variance shifts in autoregressive time series

Robert E. McCulloch, Ruey S. Tsay

Research output: Contribution to journal › Article › peer-review

114 Scopus citations

Abstract

This article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series. We first extend the analysis of random mean-shift models to random variance-shift models. We then consider a method for predicting when a shift is about to occur. This involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables. The basic computational tool we use in the proposed analysis is the Gibbs sampler. For illustration, we apply the analysis to several examples.

Original language	English (US)
Pages (from-to)	968-978
Number of pages	11
Journal	Journal of the American Statistical Association
Volume	88
Issue number	423
DOIs	https://doi.org/10.1080/01621459.1993.10476364
State	Published - Sep 1993
Externally published	Yes

Keywords

Gibbs sampler
Outlier
Probit model
Random level-shift model
Random variance-shift model
Variance change

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/01621459.1993.10476364

Cite this

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title = "Bayesian inference and prediction for mean and variance shifts in autoregressive time series",

abstract = "This article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series. We first extend the analysis of random mean-shift models to random variance-shift models. We then consider a method for predicting when a shift is about to occur. This involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables. The basic computational tool we use in the proposed analysis is the Gibbs sampler. For illustration, we apply the analysis to several examples.",

keywords = "Gibbs sampler, Outlier, Probit model, Random level-shift model, Random variance-shift model, Variance change",

author = "McCulloch, {Robert E.} and Tsay, {Ruey S.}",

note = "Funding Information: * Robert E. McCulloch is Associate Professor of Statistics and Ruey S. Tsay is Professor of Statistics, Graduate School of Business, University of Chicago, 1L 60637. This research is supported in part by National Science Foundation Grant DMS-9 103250 and by the IBM Faculty Research Fund at the Graduate School of Business, University of Chicago. The first draft of this manuscript was presented at the annual NBER/NSF Time Series Seminar in Pittsburgh in September 199 1. The authors thank the referees and an associate editor for encouraging comments.",

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AU - Tsay, Ruey S.

N1 - Funding Information: * Robert E. McCulloch is Associate Professor of Statistics and Ruey S. Tsay is Professor of Statistics, Graduate School of Business, University of Chicago, 1L 60637. This research is supported in part by National Science Foundation Grant DMS-9 103250 and by the IBM Faculty Research Fund at the Graduate School of Business, University of Chicago. The first draft of this manuscript was presented at the annual NBER/NSF Time Series Seminar in Pittsburgh in September 199 1. The authors thank the referees and an associate editor for encouraging comments.

PY - 1993/9

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N2 - This article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series. We first extend the analysis of random mean-shift models to random variance-shift models. We then consider a method for predicting when a shift is about to occur. This involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables. The basic computational tool we use in the proposed analysis is the Gibbs sampler. For illustration, we apply the analysis to several examples.

AB - This article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series. We first extend the analysis of random mean-shift models to random variance-shift models. We then consider a method for predicting when a shift is about to occur. This involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables. The basic computational tool we use in the proposed analysis is the Gibbs sampler. For illustration, we apply the analysis to several examples.

KW - Gibbs sampler

KW - Outlier

KW - Probit model

KW - Random level-shift model

KW - Random variance-shift model

KW - Variance change

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JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

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ER -

Bayesian inference and prediction for mean and variance shifts in autoregressive time series

Abstract

Keywords

ASJC Scopus subject areas

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