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function x = arma_rnd (a, b, v, t, n)
//Return a simulation of the ARMA model.
//Calling Sequence:
//arma_rnd (a, b, v, t, n)
//arma_rnd (a, b, v, t)
//Parameters:
//a: Real vector
//b: Real vector
//v: Variance
//t: Length of output vector
//n: Number of dummy x(i) used for initialization
//Description:
//The ARMA model is defined by x(n) = a(1) * x(n-1) + … + a(k) * x(n-k) + e(n) + b(1) * e(n-1) + … + b(l) * e(n-l)
//in which k is the length of vector a, l is the length of vector b and e is Gaussian white noise with variance v. The function returns a vector of length t.
//The optional parameter n gives the number of dummy x(i) used for initialization, i.e., a sequence of length t+n is generated and x(n+1:t+n) is returned.
//If n is omitted, n = 100 is used.
//Examples:
//a = [1 2 3 4 5];
//b = [7 8 9 10 11];
//v = 10;
//t = 5;
//n = 100;
//arma_rnd (a, b, v, t, n)
//Output :
// ans =
// 61400.907
// 158177.11
// 407440.29
// 1049604.
// 2703841.3
funcprot(0);
[nargout,nargin] = argn() ;
if (nargin == 4)
n = 100;
elseif (nargin == 5)
if (~ isscalar (n))
error ("arma_rnd: N must be a scalar");
end
else
error("Wrong number of input arguments.");
end
if ((min (size (a)) > 1) | (min (size (b)) > 1))
error ("arma_rnd: A and B must not be matrices");
end
if (~ isscalar (t))
error ("arma_rnd: T must be a scalar");
end
ar = length (a);
br = length (b);
a = matrix (a, ar, 1);
b = matrix (b, br, 1);
a = [1; -a];
b = [1; b];
n = min (n, ar + br);
e = sqrt (v) * rand(t + n, 1);
x = filter (b, a, e);
x = x(n + 1 : t + n);
endfunction
//input validation:
//a = [1, 2, 3, 4];
//b = [5, 6, 7];
//assert_checkerror("arma_rnd()", "Wrong number of input arguments.");
//assert_checkerror("arma_rnd(1, 2, 3, 4, 5, 6)", "Wrong number of input arguments.");
//assert_checkerror("arma_rnd(a, b, 5, 2, a);", "arma_rnd: N must be a scalar");
//assert_checkerror("arma_rnd(a, b, 5, a);", "arma_rnd: T must be a scalar");
//assert_checkerror("arma_rnd([1 2; 3 4], [5 6; 7 8], 5, 1);", "arma_rnd: A and B must not be matrices");
//tests:
//NOTE: The output of arma_rnd is supposed to be random, so we cannot expect the same output for equivalent input.
//a = [1, 2, 3, 4];
//b = [5, 6, 7, 8];
//assert_checkequal(size(arma_rnd(a, b, 5, 1)), [1 1]);
//assert_checkequal(size(arma_rnd(a, b, 5, 2, 100)), [2 1]);
//assert_checkequal(size(arma_rnd(a', b', 1, 10, 50)), [10 1]);
//assert_checkequal(size(arma_rnd(a, b', 1, 4, 5)), [4 1]);
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