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Extremes in autoregressive processes with uniform marginal distributions

Author

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  • Chernick, Michael R.
  • Davis, Richard A.

Abstract

Chernick (1981) derives a limit theorem for the maximum term for a class of first order autoregressive processes with uniform marginal distributions. The parameter [varrho] for these processes is equal to 1/r where r is an integer, r [greater-or-equal, slanted] 2. Based on this limit theorem, the asymptotic distribution of the minimum term and the joint asymptotic distribution of the maximum and minimum terms in the sequence are obtained. Since the condition D'(un) of Leadbetter (1974) fails, the condition of Davis (1979), D'(vn, un), also fails. Negatively correlated uniform sequences are shown to exist. Asymptotic distributions for the maximum and minimum terms in the sequence are derived and it is shown that the maximum and minimum are not asymptotically independent.

Suggested Citation

  • Chernick, Michael R. & Davis, Richard A., 1982. "Extremes in autoregressive processes with uniform marginal distributions," Statistics & Probability Letters, Elsevier, vol. 1(2), pages 85-88, November.
    • Handle: RePEc:eee:stapro:v:1:y:1982:i:2:p:85-88
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    Cited by:

    1. Ristic, Miroslav M. & Popovic, Biljana C., 2002. "The uniform autoregressive process of the second order (UAR(2))," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 113-119, April.
    2. Christopher Withers & Saralees Nadarajah, 2011. "The distribution of the maximum of a first order autoregressive process: the continuous case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 247-266, September.
    3. Mladenovic, Pavle, 2009. "Maximum of a partial sample in the uniform AR(1) processes," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1414-1420, June.

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