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Linear serial rank tests for randomness against ARMA alternatives. (English) Zbl 0584.62064
This is a systematic and quite thorough study of testing whether a time series may be regarded as independent (random) or whether it has an ARMA type of dependency. The test statistic being used is a sum of suitable score functions of the ranks of the successive observations. With special choices for the score functions a number of the known test statistics are obtained. The efficiency properties of the proposed statistics are investigated, and a formulation of the asymptotically most efficient score is given.
Reviewer: J.Rissanen

MSC:
62G10 Nonparametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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