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// Copyright (C) 2018 - IIT Bombay - FOSSEE
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
// Author:[insert name]
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in
function [A,V]= yulewalker(c)
// Fit an AR (p)-model with Yule-Walker estimates given a vector C of autocovariances '[gamma_0, ..., gamma_p]'.
//Calling Sequence
//A = yulewalker(C)
//[A,V]= yulewalker(C)
//Parameters
//C: Autocovariances
//Description
//Fit an AR (p)-model with Yule-Walker estimates given a vector C of autocovariances '[gamma_0, ..., gamma_p]'.
//Returns the AR coefficients, A, and the variance of white noise, V.
//Test cases
//[A,V]=yulewalker([1 2 3])
// V = - 2.6666667
// A =1.3333333
// 0.3333333
funcprot(0);
lhs=argn(1);
rhs= argn(2);
if (rhs ~= 1)
error ("wrong number of input arguments");
end
p = length (c) - 1;
if (size (c,"c") > 1)
c = c';
end
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);
end
end
A = inv (CP) * cp;
V = c(1) -A' * cp;
endfunction
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