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Order Patterns in Time Series

2007; Wiley; Volume: 28; Issue: 5 Linguagem: Inglês

10.1111/j.1467-9892.2007.00528.x

1467-9892

Christoph Bandt, F. A. Shiha,

Time Series Analysis and Forecasting

Abstract. 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.