The Annals of Statistics

Linear Serial Rank Tests for Randomness Against Arma Alternatives

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

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In this paper we introduce a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence. The asymptotic normality of the proposed statistics is established, both under the null as well as alternative hypotheses, using LeCam's notion of contiguity. The efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided. Finally, we study the asymptotic relative efficiency of the proposed procedures with respect to their normal theory counterparts based on sample autocorrelations.

Article information

Ann. Statist., Volume 13, Number 3 (1985), 1156-1181.

First available in Project Euclid: 12 April 2007

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Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G10: Hypothesis testing

Linear serial rank statistics autoregressive moving average ARMA models asymptotic relative efficiency


Hallin, Marc; Ingenbleek, Jean-Francois; Puri, Madan L. Linear Serial Rank Tests for Randomness Against Arma Alternatives. Ann. Statist. 13 (1985), no. 3, 1156--1181. doi:10.1214/aos/1176349662.

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