ESTIMATION FOR NONNEGATIVE AUTOREGRESSIVE PROCESSES WITH AN UNKNOWN LOCATION PARAMETER

William P. McCormick and George Mathew

Journal of Time Series Analysis, 1993, vol. 14, issue 1, 71-92

Abstract: Abstract. Consider an AR(1) process given by Xt=γ+øXt+Zt≥ 1. where 0 ≤γ, 0 ≤ø 1 are unknown parameters and the innovations Zt, ≥ 1, are independently and identically distributed positive random variables. We propose estimates of (γø) which are obtained as the solution to a linear programming problem and establish their strong consistency. When the Zts have the exponential distribution. our estimate becomes the conditional maximum likelihood estimate given X0. Under the assumption of regular variation of the innovation distribution at its left and right endpoints (assumed to be 0 and ∝ respectively), we establish asymptotic limit laws for the estimates. Consistent estimators for a class of moving‐average processes with heavy‐tailed innovation distribution are also presented.

Date: 1993
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https://doi.org/10.1111/j.1467-9892.1993.tb00130.x

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Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:14:y:1993:i:1:p:71-92

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