Efficiencies of tests and estimators for p-order autoregressive processes when the error distribution is nonnormal

Michael G. Akritas, Richard A. Johnson

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We consider pth order autoregressive time series where the shocks need not be normal. By employing the concept of contiguity, we obtain the sysmptotic power for tests of hypothesis concerning the autoregressive parameters. Our approach allows consideration of the double exponential and other thicker-tailed distributions for the shocks. We derive a new result in the contiguity framework that leads directly to an expression for the Pitman efficiencies of tests as well as estimators. The numerical values of the efficiencies suggest a lack of robustness for the normal theory least squares estimators when the shock distribution is thick tailed or an outlier prone mixed normal. An important alternative test statistic is proposed that competes with the normal theory tests.

Original languageEnglish (US)
Pages (from-to)579-589
Number of pages11
JournalAnnals of the Institute of Statistical Mathematics
Volume34
Issue number1
DOIs
StatePublished - Dec 1 1982

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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