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March, 1988 Optimal Rank-Based Procedures for Time Series Analysis: Testing an ARMA Model Against Other ARMA Models
Marc Hallin, Madan L. Puri
Ann. Statist. 16(1): 402-432 (March, 1988). DOI: 10.1214/aos/1176350712

Abstract

The problem of testing a given ARMA model (in which the density of the generating white noise is unspecified) against other ARMA models is considered. A distribution-free asymptotically most powerful test, based on a generalized linear serial rank statistic, is provided against contiguous ARMA alternatives with specified coefficients. In the case when the ARMA model in the alternative has unspecified coefficients, the asymptotic sufficiency (in the sense of Le Cam) of a finite-dimensional vector of rank statistics is established. This asymptotic sufficiency is used to derive an asymptotically maximin most powerful test, based on a generalized quadratic serial rank statistic. The asymptotically maximin optimal test statistic can be interpreted as a rank-based, weighted version of the classical Box-Pierce portmanteau statistic, to which it reduces, in some particular problems, asymptotically and under Gaussian assumptions.

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Marc Hallin. Madan L. Puri. "Optimal Rank-Based Procedures for Time Series Analysis: Testing an ARMA Model Against Other ARMA Models." Ann. Statist. 16 (1) 402 - 432, March, 1988. https://doi.org/10.1214/aos/1176350712

Information

Published: March, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0659.62111
MathSciNet: MR924878
Digital Object Identifier: 10.1214/aos/1176350712

Subjects:
Primary: 62M10
Secondary: 62G10

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 1 • March, 1988
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