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P. J. Brockwell and R. A Davis, “Time Series: Theory and Methods,” 2nd Edition, Springer, New York, 1987.

has been cited by the following article:

• TITLE: Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter

  AUTHORS: Andrew Bartlett, William McCormick

  KEYWORDS: Nonnegative Time Series; Autoregressive Processes; Extreme Value Estimator; Regular Variation; Point Processes

  JOURNAL NAME: Applied Mathematics, Vol.3 No.12A, December 31, 2012

  ABSTRACT: Consider a first-order autoregressive processes , where the innovations are nonnegative random variables with regular variation at both the right endpoint infinity and the unknown left endpoint θ. We propose estimates for the autocorrelation parameter f and the unknown location parameter θ by taking the ratio of two sample values chosen with respect to an extreme value criteria for f and by taking the minimum of over the observed series, where represents our estimate for f. The joint limit distribution of the proposed estimators is derived using point process techniques. A simulation study is provided to examine the small sample size behavior of these estimates.