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Bayesian analysis of an autoregressive process with exponential white noise. (English) Zbl 0723.62051

Summary: The object of this paper is a Bayesian analysis of the autoregressive model \(X_ t=\rho X_{t-1}+Y_ t\), where \(0\leq \rho <1\) and \(Y_ t\) are independent random variables with an exponential distribution. Bayesian estimates are obtained and are shown to be equivalent, for large samples, to a modification of the maximum likelihood estimates suggested by J. Anděl [Commun. Stat., Theory Methods 17, No.5, 1481-1495 (1988; Zbl 0639.62082)]. Also 100(1-\(\alpha\))% HPD credible sets for \(\rho\) are obtained. The problem of predicting future events is also considered.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F15 Bayesian inference

Citations:

Zbl 0639.62082
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References:

[1] DOI: 10.1017/CBO9780511569647 · doi:10.1017/CBO9780511569647
[2] DOI: 10.1080/03610928808829693 · Zbl 0639.62082 · doi:10.1080/03610928808829693
[3] Andel J., Kyhernetiha 24 pp 372– (1988)
[4] DOI: 10.1080/03610928608829248 · Zbl 0604.62087 · doi:10.1080/03610928608829248
[5] DOI: 10.1007/978-1-4757-4286-2 · doi:10.1007/978-1-4757-4286-2
[6] DOI: 10.2307/1426429 · Zbl 0453.60048 · doi:10.2307/1426429
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