Rank-Based Autoregressive Order Identification
作者:
Bernard Garel,
Marc Hallin,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1999)
卷期:
Volume 94,
issue 448
页码: 1357-1371
ISSN:0162-1459
年代: 1999
DOI:10.1080/01621459.1999.10473887
出版商: Taylor & Francis Group
关键词: Autoregressive model;Order identification;Rank test;Robust methods;Time series.
数据来源: Taylor
摘要:
Optimal rank-based procedures have been derived for testing arbitrary linear restrictions on the parameters of autoregressive moving average (ARMA) models with unspecified innovation densities. The finite-sample performances of these procedures are investigated here in the context of AR order identification and compared to those of classical (partial correlograms and Lagrange multipliers) methods. The results achieved by rank-based methods are quite comparable, in the Gaussian case, to those achieved by the traditional ones, which, under Gaussian assumptions, are asymptotically optimal. However, under non-Gaussian innovation densities, especially heavy-tailed or nonsymmetric, or when outliers are present, the percentages of correct order selection based on rank methods are strikingly better than those resulting from traditional approaches, even in the case of very short (n= 25) series. These empirical findings confirm the often ignored theoretical fact that the Gaussian case, in the ARMA context, is the least favorable one. The robustness properties of rank-based identification methods are also investigated; it is shown that, contrary to the robustified versions of their classical counterparts, the proposed rank-based methods are not affected, neither by the presence of innovation outliers nor by that of observation (additive) outliers.
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