Open Access
April 2003 Efficient detection of random coefficients in autoregressive models
Abdelhadi Akharif, Marc Hallin
Ann. Statist. 31(2): 675-704 (April 2003). DOI: 10.1214/aos/1051027885


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.


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Abdelhadi Akharif. Marc Hallin. "Efficient detection of random coefficients in autoregressive models." Ann. Statist. 31 (2) 675 - 704, April 2003.


Published: April 2003
First available in Project Euclid: 22 April 2003

zbMATH: 1039.62081
MathSciNet: MR1983546
Digital Object Identifier: 10.1214/aos/1051027885

Primary: 62G10 , 62M10

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

Rights: Copyright © 2003 Institute of Mathematical Statistics

Vol.31 • No. 2 • April 2003
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