Distributions of order patterns in time series

Summary. Recent use of order patterns in time series analysis shows the need for a corre-sponding theory. We determine probabilities of order patterns in Gaussian and ARMA pro-cesses. Two order functions are introduced which characterize a time series in a similar way as 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. 1