NAME

       gbacorr - Compute auto/cross-correlation coefficients

SYNOPSIS

       gbacorr [options]

DESCRIPTION

       Compute auto/cross-correlation coefficients

       If  the input is a single columns x_1...X_T, the autocorrelation function c(t) is printed,
       defined as

              c_{t} = 1/(T-t-1) \sum_i (x_i-m) (x_{i+t}-m) /s^2

       where m is the sample average  and  s  the  standard  deviation.   With  a  second  column
       y_1...y_T, the cross-correlation

              c_{t} = 1/(T-t-1) \sum_i (x_i-mx) (y_{i+t}-my) /(sx sy)

       is  printed  where mx and my are the average values of the two columns and sx and sy their
       standard deviations. With -M 1 it is mx=my=0, the st.dev. is computed accordingly  and  in
       the  previous  formula  T-t-1  is  replaced  by  T-t.  The range of t is set by option -t.
       Options

       -M     choose the method (default '0'):

       0      auto/cross-correlation with mean removal,

       1      auto/cross-correlation without mean removal

       -t     set range of t (default '0,10'), accept negative integers

       -p     specify the confidence level in (0,1).  Interval  ac_low,ac_hi  has  a  probability
              1-confidence to contain the true value. With this option the output becomes: lag ac
              ac_low ac_hi.

       -F     specify the input fields separators (default " \t")

       -h     this help

EXAMPLES

       gbacorr -t 0,2 'file(1)'
              first three a.c. coeff. of the first data column

       gbacorr -p 0.05 'file(1:2)' x-corr of the first two columns together with
              their 5% confidence intervals

AUTHOR

       Written by Giulio Bottazzi

REPORTING BUGS

       Report bugs to <gbutils@googlegroups.com>

       Package home page <http://cafim.sssup.it/~giulio/software/gbutils/index.html>

COPYRIGHT

       Copyright © 2001-2018 Giulio Bottazzi This program is free software; you can  redistribute
       it  and/or  modify  it  under  the  terms of the GNU General Public License (version 2) as
       published by the Free Software Foundation;

       This program is distributed in the hope that it will be useful, but WITHOUT ANY  WARRANTY;
       without  even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
       See the GNU General Public License for more details.