The Annals of Statistics

Optimal Rank-Based Procedures for Time Series Analysis: Testing an ARMA Model Against Other ARMA Models

Marc Hallin and Madan L. Puri

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 16, Number 1 (1988), 402-432.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350712

Digital Object Identifier
doi:10.1214/aos/1176350712

Mathematical Reviews number (MathSciNet)
MR924878

Zentralblatt MATH identifier
0659.62111

JSTOR
links.jstor.org

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

Keywords
ARMA models linear serial rank statistics quadratic rank statistics rank portmanteau statistics asymptotic sufficiency asymptotically most powerful tests asymptotically maximin most powerful tests

Citation

Hallin, Marc; Puri, Madan L. Optimal Rank-Based Procedures for Time Series Analysis: Testing an ARMA Model Against Other ARMA Models. Ann. Statist. 16 (1988), no. 1, 402--432. doi:10.1214/aos/1176350712. https://projecteuclid.org/euclid.aos/1176350712


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