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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.