Distributions Of Order Patterns in Time Series

Distributions of Order Patterns in Time Series presents a simple, fast and robust method of time series analysis, the basic idea is to consider the order relations among the values of a time series instead of the the values themselves, we determined analytically probabilities of order patterns of asymmetric periodic sawtooth function, Gaussian and ARMA processes, fractional Brownian motion, we estimate the probabilities of the order patterns of many empirical time series and extract many basic features of the series from the behavior of the order patterns. In the end the book presents the permutation entropy as a measure of complexity of time series. The book is useful as a text for graduate-level in Mathematics ( probability and statistics) and Physics