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Biometrika 1967 54(1-2):39-68; doi:10.1093/biomet/54.1-2.39
© 1967 by Biometrika Trust
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Some tests of separate families of hypotheses in time series analysis

A. M. WALKER

Statistical Laboratory, University of Cambridge

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.


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