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########################################################################
##
## Copyright (C) 1995-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {[@var{a}, @var{v}] =} yulewalker (@var{c})
## Fit an AR (p)-model with Yule-Walker estimates given a vector @var{c} of
## autocovariances @code{[gamma_0, @dots{}, gamma_p]}.
##
## Returns the AR coefficients, @var{a}, and the variance of white noise,
## @var{v}.
## @end deftypefn
function [a, v] = yulewalker (c)
if (nargin < 1)
print_usage ();
endif
p = length (c) - 1;
if (columns (c) > 1)
c = c';
endif
cp = c(2 : p+1);
CP = zeros (p, p);
for i = 1:p
for j = 1:p
CP (i, j) = c (abs (i-j) + 1);
endfor
endfor
a = inv (CP) * cp;
v = c(1) - a' * cp;
endfunction
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