gbacorr - Compute auto/cross-correlation coefficients

       Written by Giulio Bottazzi

       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.

gbacorr 6.2                                         June 2021                                         GBACORR(1)

       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

       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

       gbacorr - Compute auto/cross-correlation coefficients

       Report bugs to <gbutils@googlegroups.com>

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

gbacorr [options]