Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter - Applied Mathematics

AM > Vol.3 No.12, December 2012

Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter ()

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DOI: 10.4236/am.2012.312A294 3,856 Downloads 6,337 Views Citations

Author(s)

Andrew Bartlett, William McCormick

Affiliation(s)

University of Georgia, Athens, USA.

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.

KEYWORDS

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

Share and Cite:

A. Bartlett and W. McCormick, "Estimation for Nonnegative First-Order Autoregressive Processes with an Unknown Location Parameter," Applied Mathematics, Vol. 3 No. 12A, 2012, pp. 2133-2147. doi: 10.4236/am.2012.312A294.

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