Extremes in autoregressive processes with uniform marginal distributions

Michael R. Chernick and Richard A. Davis

Statistics & Probability Letters, 1982, vol. 1, issue 2, 85-88

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.

Keywords: Asymptotic; theory; maxima; minima; midrange; range; stationary; sequences; uniform; AR(1); processes (search for similar items in EconPapers)
Date: 1982
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Citations: View citations in EconPapers (3)

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