The Annals of Statistics
- Ann. Statist.
- Volume 13, Number 3 (1985), 1156-1181.
Linear Serial Rank Tests for Randomness Against Arma Alternatives
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.
Ann. Statist., Volume 13, Number 3 (1985), 1156-1181.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G10: Hypothesis testing
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. https://projecteuclid.org/euclid.aos/1176349662