Rank-Based Tests for Randomness Against First-Order Serial Dependence.

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the finite-sample behavior of the asymptotically optimal tests for randomness against first-order autoregressive moving average dependence proposed in Hallin et al. (1985), both under the null hypothesis (tables of critical values) and under alternatives of serial dependence (evaluation of the power function), and (b) an (heuristic) investigation of the robustness properties of the proposed procedures (with emphasis on the identification problem in the presence of "outliers"). We begin (Sec. 2) with a brief description of the rank-based measures of serial dependence to be considered throughout: (a) Van der Waerden, (b) Wilcoxon, (c) Laplace, and (d) Spearman-Wald-Wolfowitz autocorrelations. The article is mainly concerned with first-order (lag 1) coefficients of these types. Tables of the critical values required for performing tests of randomness are provided (Sec. 3), and the finite-sample power of the resulting tests is compared with that of their parametric competitors (Sec. 4). Although the exact level of classical parametric procedures is only approximately correct (whereas the distribution-free rank tests are of the correct size), the proposed rank-based tests compare quite favorably with the classical ones, and appear to perform at least as well as (often strictly better than) their classical counterparts. The examples of Section 5 emphasize the... [ABSTRACT FROM AUTHOR]