Journal
JOURNAL OF TIME SERIES ANALYSIS
Volume 28, Issue 5, Pages 646-665Publisher
BLACKWELL PUBLISHING
DOI: 10.1111/j.1467-9892.2007.00528.x
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Recent use of order patterns in time-series analysis shows the need for a corresponding theory. We determine probabilities of order patterns in Gaussian and autoregressive moving-average (ARMA) processes. Two order functions are introduced which characterize a time series in a way similar to autocorrelation. For stationary ergodic processes, all finite-dimensional distributions are obtained from the one-dimensional distribution plus the order structure of a typical time series.
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