Rank-based autoregressive order identification

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.