    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   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 'm' option makes no sense if a presumed mean is specified.

    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) 1995-2003 by Radford M. Neal