Time series analysis via rank order theory: Signed-rank tests for ARMA models

An asymptotic distribution theory is developed for a general class of signed-rank serial statistics, and is then used to derive asymptotically locally optimal tests (in the maximin sense) for testing an ARMA model against other ARMA models. Special cases yield Fisher-Yates, van der Waerden, and Wilcoxon type tests. The asymptotic relative efficiencies of the proposed procedures with respect to each other, and with respect to their normal theory counterparts, are provided.