Hallin, Marc; Melard, Guy Les statistiques de rangs dans l’identification de modèles de séries chronologiques. (Rank statistics for time series model identification). (French) Zbl 0607.62110 Cah. Cent. Étud. Rech. Opér. 28, 117-129 (1986). This paper contains a study of the sampling fluctuations of the rank autocorrelations and of linear and quadratic statistics made of rank autocorrelations, such as the rank ”portmanteau” statistics. The main purpose of this study, which includes Monte-Carlo simulations, is to establish whether some asymptotic distributional results on rank correlations and statistics thereof, apply reasonably well to small or medium sized samples. The problem of testing the null hypothesis that the process under study is a white noise, against the alternative hypothesis that it is an ARMA process, is also investigated. The power of some linear and quadratic tests based on rank correlations is analysed in the small-sample case, and compared to the power of the corresponding tests based on serial correlations. Several applications to real-life data are included which (also) support the view that the rank correlation-based tests are more robust to outlier data than the corresponding tests based on the usual serial correlations. Reviewer: P.Stoica MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M07 Non-Markovian processes: hypothesis testing 62G10 Nonparametric hypothesis testing 65C99 Probabilistic methods, stochastic differential equations Keywords:model identification; van der Waerden type test; Wilcoxon type test; median type test; rank portmanteau statistics; sampling fluctuations; rank autocorrelations; linear and quadratic statistics; Monte-Carlo simulations; asymptotic distributional results; small or medium sized samples; white noise; ARMA process; power; linear and quadratic tests based on rank correlations; tests based on serial correlations; robust; outlier data PDFBibTeX XMLCite \textit{M. Hallin} and \textit{G. Melard}, Cah. Cent. Étud. Rech. Opér. 28, 117--129 (1986; Zbl 0607.62110)