The Annals of Statistics
- Ann. Statist.
- Volume 16, Number 1 (1988), 402-432.
Optimal Rank-Based Procedures for Time Series Analysis: Testing an ARMA Model Against Other ARMA Models
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.
Ann. Statist., Volume 16, Number 1 (1988), 402-432.
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
ARMA models linear serial rank statistics quadratic rank statistics rank portmanteau statistics asymptotic sufficiency asymptotically most powerful tests asymptotically maximin most powerful tests
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