Some tests of separate families of hypotheses in time series analysis

1 June 1967

journal article
Published by Oxford University Press (OUP) in Biometrika

Vol. 54 (1-2) , 39-68
https://doi.org/10.1093/biomet/54.1-2.39

Abstract

This paper deals with the application to various problems in time series analysis of the maximum-likelihood ratio procedure proposed by Cox for situations in which there are rival hypotheses H₀ and H₁, such that probabifity distributions of data under H₀ and H₁ constitute ‘separate’ parametric families. The large-sample theory developed by Cox, outlined in §2, is extended to two main types of problem. In the first, the time series is generated by an autoregression of specified order p under one hypothesis and by a movingaverage of specified order q under the other; the particular case p = q = 1 is treated in §3 and the general case in §4. In the second, the series is generated by a simple harmonic oscillation with superimposed random error under one hypothesis and by an autoregression under the other; this is treated in §5. More general types of problem are considered in §6, but for these the computations required by the procedure may be impracticable.

Keywords

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