Linear serial rank tests for randomness against ARMA alternatives. (English) Zbl 0584.62064

Hallin, Marc; Ingenbleek, Jean-Francois; Puri, Madan L.

Ann. Stat. 13, 1156-1181 (1985).

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)

Keywords:

linear serial rank tests for randomness; asymptotic normality; contiguity; asymptotic relative efficiency; autoregressive moving average; time series; ARMA type of dependency; score functions of the ranks of the successive observations; asymptotically most efficient score