SERIES: Analyse stationary time series data. Series reads time series data from standard input and outputs various statistics on standard output. Usage: series options [ max-lag [ presumed-mean ] ] <data The data read from standard input consists of one or more realizations of the time series. Each point from the series is given by a single real number, with each number being the first field of a line (with any following fields ignored). The different realizations are separated by blank lines. The options control what statistics are printed, as follows: m Sample mean, with standard error s Standard deviation v Variance a Autocorrelations up to the given maximum lag c Cumulative autocorrelations up to the given maximum lag. At lag i, the cumulative autocorrelation is one plus twice the sum of the autocorrelations from 1 to i. b Print only the bare autocorrelations and/or cumulative autocorrelations, labelled by lag, without headings. Output consists of lines containing the lags, in increasing order from one, and the autocorrelation and/or the cumulative autocorrelation, in that order. e Do nothing except echo the data read on standard output. (Meant for use in testing.) The standard error of the mean is calculated in two ways - from the sub-means for the various realizations (if there is more than one, and they are all the same length), and from the cumulative autocorrelations (if a maximum lag is given). The default maximum lag is the maximum length of any of the realizations minus one. If a presumed mean is specified, it is used rather than the estimated mean when calculating the autocorrelations, and the displayed variance, and the variance used to normalize the autocorrelations. The sample mean can still be displayed with the 'm' option, but it is not used for other calculations. The autocovariance estimate at lag k is calculated from a series of length n using a divisor of n-k, not n (as is sometimes done). The variance is calculated with a divisor of n, but the standard error from sub-means uses a divisor of number-of-realizations - 1. Copyright (c) 1995-2004 by Radford M. Neal