Rank-based autoregressive order identification

Optimal-rank-based procedures have been derived for testing arbitrary linea r restrictions on the parameters of autoregressive moving average (ARMA) mo dels with unspecified innovation densities. The finite-sample performances of these procedures are investigated here in the context of AR order identi fication and compared to those of classical (partial correlograms and Lagra nge multipliers) methods. The results achieved by rank-based methods are qu ite comparable, in the Gaussian case, to those achieved by the traditional ones, which, under Gaussian assumptions, are asymptotically optimal. Howeve r, under non-Gaussian innovation densities, especially heavy-tailed or nons ymmetric, or when outliers are present, the percentages of correct order se lection based on rank methods are strikingly better than those resulting fr om traditional approaches, even in the case of very short (n = 25) series. These empirical findings confirm the often ignored theoretical fact that th e Gaussian case, in the ARMA context, is the least favorable one. The robus tness 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.