Question

I am trying to generate an array from some starting values using this formula in MATLAB:

y_t = a₀ + ∑_i=1^p (a_i ⋅ y_t-i), t ≥ p

p is some small number compared to T (max t). I have been able to make this using two for cycles but it is really slow. Is there some easy way to do it?

First p values of y are provided and vector a (its length is p+1) is provided too…

This is what I have so far, but now when I tried it, it doesn’t work 100% (I think it’s because of indexing from 1 in MATLAB):

y1 = zeros(T+1, 1);
y1(1:p) = y(1:p);

for t = p+1:T+1
    value = a1(1);
    for j = 2:p+1
        value = value + a1(j)*y1(t-j+1);
    end
    y1(t) = value;
end

EDIT: I solved it, I am just not used to Matlab indexing from 1…

Answer 1

y1 = zeros(T+1, 1);
y1(1:p) = y(1:p);

for t = p+1:T+1
    value = a1(1);
    for j = 2:p+1
        value = value + a1(j)*y1(t-j+1);
    end
    y1(t) = value;
end