Abstract

Abstract Let Xt, t=…,−1,0,1,…, be a strictly stationary time series and X1,…,Xn be n consecutive observations of Xt. Let Rnt denote the rank of Xt among the Xt's, 1≤t≤n. Consider the vector of serial rank statistics T n =(T 1 n ,…,T p n )′ , where Jn and Ln are score functions. joint asymptotic multivariate normality of Tn is obtained under general fixed serially dependent alternatives. The asymptotic distributions of various serial rank statistics are obtained as consequences. Some applications are considered.

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