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ORDER STATISTICS FOR NONSTATIONARY TIME SERIES

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LANH TAT TRAN^{1} AND BERLIN WU^{2}

^{1} *Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.*

^{2} *National Chengchi University, Taipei, Taiwan*
(Received October 23, 1991; revised October 6, 1992)

**Abstract.**
Order statistics has an important role in statistical
inference. The main purpose of this paper is to investigate order
statistics, and
also explore its applications in the analysis of nonstationary time
series. Our results show that linear functions of order statistics
for a large class of time series are asymptotically normal. The
methods of proof involve approximations of serially dependent random
variables by independent ones. The problems of testing for the
existence of a linear trend and the problem of testing randomness
versus serial dependence are considered as applications.

*Key words and phrases*:
Nonstationary, autoregressive processes,
absolute regularity, empirical distribution functions, order
statistics.

**Source**
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