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On AR(1) processes with exponential white noise. (English) Zbl 0639.62082

Summary: We consider the autoregressive model \(X_ t=bX_{t-1}+Y_ t\) where \(0\leq b<1\) and \(Y_ t\) are independent random variables with an exponential distribution. The moments of the stationary distribution of \(X_ t\) are calculated and the distribution of an approximation to the maximum likelihood estimator for b is derived. The result is used for a construction of a confidence interval for b.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F10 Point estimation
62E15 Exact distribution theory in statistics
62E20 Asymptotic distribution theory in statistics
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References:

[1] Andel J., Journal of Time Series Analysis (1987)
[2] DOI: 10.1080/03610928608829248 · Zbl 0604.62087 · doi:10.1080/03610928608829248
[3] DOI: 10.2307/1426429 · Zbl 0453.60048 · doi:10.2307/1426429
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