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fractdiff.m

## Copyright (C) 1995, 1996, 1997  Friedrich Leisch
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
## 
## 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. 
## 
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  fractdiff(x, d)
##
## Computes the fractional differences (1-L)^d x where L denotes the
## lag-operator and d > -1.
  
## Author:  FL <Friedrich.Leisch@ci.tuwien.ac.at>
## Description:  Compute fractional differences
    
function retval = fractdiff (x, d)
    
  N = 100;
  
  if !is_vector (x)
    error ("fractdiff:  x must be a vector")
  endif
  
  if !is_scalar (d)
    error ("fractdiff:  d must be a scalar")
  endif
  
    
  if (d >= 1)
    for k = 1 : d
      x = x(2 : length (x)) - x(1 : length (x) - 1);
    endfor
  endif
  
  if (d > -1)
    
    d = rem (d, 1);
  
    if (d != 0)
      n = (0 : N)';
      w = real (gamma (-d+n) ./ gamma (-d) ./ gamma (n+1));
      retval = fftfilt (w, x);
      retval = retval(1 : length (x));
    else
      retval = x;
    endif
    
  else
    error ("fractdiff:  d must be > -1");
    
  endif
  
endfunction

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