Abstract
Abstract It is shown that in the case of stationary m-dependent processes, the J-th (J≥1) record times {Tn,n≥1} and the corresponding J-upper statistics {XTn−J+1, Tn,…,XTn,Tn} can almost surely be identified via a translation of the time index n to the corresponding elements defined on a sequence of independent and identically distributed random variables. A construction method of approximating sequences of record times and the corresponding upper order statistics introduced by Haiman (1987a) for the case J=1 is extended and applied under a weaker condition concerning the joint distribution of (X1,X1), i=2,…,m.
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