How to efficiently get covariance matrices from a rolling window in Matlab?

Question

I'am trying to produce a rolling window to estimate a covariance matrix using a for-loop. I have my returns under the variable returns_sec and I have 260 observations stored under N_ret.

I now want to produce a covariance matrix estimate based on ten return series at a time and obtain one big variable with all covariance matrices in it (Top lines: Matrix1, below Matrix2 and so on).

I could to this by hand by writing:

kov_test=cov(returns_sec(1:10,:));  
kov_test2=cov(returns_sec(11:21,:));  ...

and copy all results in one variable. But I think there should also be a more effective and easy way using a for-loop.

Would be great if anyone of you could help me out!

Answer 1

I would recommend you to use rolling overlapping window (1st implementation) instead of non-overlapping (your example - 2nd implementation)

% overlapping rolling covariance
[n,m] = size(returns_sec); % n-> number of dates, m->number of assets
rolling_window = 10;
cov_test = nan(m*(n - rolling_window + 1),m);
for i = rolling_window:n
    start_index = m*(i - rolling_window) + 1; % aggregate covariance matrix start index
    end_index = m*(i - rolling_window +1); % aggregate covariance matrix end index
    covariance_mtx = cov(returns_sec(i-rolling_window +1:i,:));
    cov_test(start_index:end_index,:) = covariance_mtx;
end

% non-overlapping rolling covariance
[n,m] = size(returns_sec); % n-> numberg of dates, m->number of assets
rolling_window = 10;
num = floor(n/rolling_window); % number of non-overllaping intervals
cov_test = nan(m*num,m);
for i = 1:num
    start_index = m*(i - 1) + 1; % aggregate covariance matrix start index
    end_index = m*i; % aggregate covariance matrix end index
    covariance_mtx = cov(returns_sec(rolling_window*(i - 1) + 1: rolling_window*i,:));
    cov_test(start_index:end_index,:) = covariance_mtx;
end