update packages

[CreaPhase.git] / octave_packages / m / signal / diffpara.m

diff --git a/octave_packages/m/signal/diffpara.m b/octave_packages/m/signal/diffpara.m
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+## Copyright (C) 1995-2012 Friedrich Leisch
+##
+## This file is part of Octave.
+##
+## Octave 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 3 of the License, or (at
+## your option) any later version.
+##
+## Octave 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 Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{d}, @var{dd}] =} diffpara (@var{x}, @var{a}, @var{b})
+## Return the estimator @var{d} for the differencing parameter of an
+## integrated time series.
+##
+## The frequencies from @math{[2*pi*a/t, 2*pi*b/T]} are used for the
+## estimation.  If @var{b} is omitted, the interval
+## @math{[2*pi/T, 2*pi*a/T]} is used.  If both @var{b} and @var{a} are
+## omitted then @math{a = 0.5 * sqrt (T)} and @math{b = 1.5 * sqrt (T)}
+## is used, where @math{T} is the sample size.  If @var{x} is a matrix,
+## the differencing parameter of each column is estimated.
+##
+## The estimators for all frequencies in the intervals
+## described above is returned in @var{dd}.  The value of @var{d} is
+## simply the mean of @var{dd}.
+##
+## Reference: P.J. Brockwell & R.A. Davis. @cite{Time Series:
+## Theory and Methods}. Springer 1987.
+## @end deftypefn
+
+## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at>
+## Description: Estimate the fractional differencing parameter
+
+function [d, dd] = diffpara (x, a, b)
+
+  if ((nargin < 1) || (nargin > 3))
+    print_usage ();
+  else
+    if (isvector (x))
+      n = length (x);
+      k = 1;
+      x = reshape (x, n, 1);
+    else
+      [n, k] = size(x);
+    endif
+    if (nargin == 1)
+      a = 0.5 * sqrt (n);
+      b = 1.5 * sqrt (n);
+    elseif (nargin == 2)
+      b = a;
+      a = 1;
+    endif
+  endif
+
+  if (! (isscalar (a) && isscalar (b)))
+    error ("diffpara: A and B must be scalars");
+  endif
+
+  dd = zeros (b - a + 1, k);
+
+  for l = 1:k
+
+    w = 2 * pi * (1 : n-1) / n;
+
+    x = 2 * log (abs (1 - exp (-i*w)));
+    y = log (periodogram (x(2:n,l)));
+
+    x = center (x);
+    y = center (y);
+
+    for m = a:b
+      dd(m-a+1) = - x(1:m) * y(1:m) / sumsq (x(1:m));
+    endfor
+
+  endfor
+
+  d = mean (dd);
+
+endfunction
+