Efficient evaluation of Auto Regressive Covariance matrix

I need to improve the calculation of the following Covariance matrix (C), where p is the order of an autoregressive model and x(istart:istop) is the time series for which I would like to have C:

for i=0:p

for j=0:i

sum_=0;

for t=p+istart:istop

sum_ = sum_ + x(t-i)*x(t-j);

end

C(i+1,j+1)=sum_;

end

end

Answer 1

[Shubham Rawat]

Hi Sebastiano,

You can do the following things to evaluate efficiently,

• You can pre-initialize the Covariance(C) matrix by zeros or ones.

C = zeros(p+1,p+1);

• You can Vectorize the code for specific tasks.

t = p+istart:istop;
cumulative_sum = cumsum(x(t-i).*x(t-j));
sum_ = cumulative_sum(last_element);

• You can also parallelize the for loop by using parfor.

parfor t = p+istart:istop