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.