The Annals of Statistics

Efficient detection of random coefficients in autoregressive models

Abdelhadi Akharif and Marc Hallin

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Abstract

The problem of detecting randomness in the coefficients of an AR(p) model, that is, the problem of testing ordinary AR(p) dependence against the alternative of a random coefficient autoregressive [RCAR(p)] model is considered. A nonstandard LAN property is established for RCAR(p) models in the vicinity of AR(p) ones. Two main problems arise in this context. The first problem is related to the statistical model itself: Gaussian assumptions are highly unrealistic in a nonlinear context, and innovation densities should be treated as nuisance parameters. The resulting semiparametric model however appears to be severely nonadaptive. In contrast with the linear ARMA case, pseudo-Gaussian likelihood methods here are invalid under non-Gaussian densities; even the innovation variance cannot be estimated without a strict loss of efficiency. This problem is solved using a general result by Hallin and Werker, which provides semiparametrically efficient central sequences without going through explicit tangent space calculations. The second problem is related to the fact that the testing problem under study is intrinsically one-sided, while the case of multiparameter one-sided alternatives is not covered by classical asymptotic theory under LAN. A concept of locally asymptotically most stringent somewhere efficient test is proposed in order to cope with this one-sided nature of the problem.

Article information

Source
Ann. Statist., Volume 31, Number 2 (2003), 675-704.

Dates
First available in Project Euclid: 22 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1051027885

Digital Object Identifier
doi:10.1214/aos/1051027885

Mathematical Reviews number (MathSciNet)
MR1983546

Zentralblatt MATH identifier
1039.62081

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

Keywords
Random coefficient autoregressive models local asymptotic normality one-sided multiparameter tests one-sided multiparameter alternatives

Citation

Akharif, Abdelhadi; Hallin, Marc. Efficient detection of random coefficients in autoregressive models. Ann. Statist. 31 (2003), no. 2, 675--704. doi:10.1214/aos/1051027885. https://projecteuclid.org/euclid.aos/1051027885


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