Calculating cross correlation for non-consecutive lags

I have two very large vectors, T and h, each element spaced 0.01 months apart from the previous one, for a total period of 100 years, which makes a length of 120000 elements. I am interested in calculating the cross-correlation up to 10 years (120 months), but I only need to calculate it for lags multiple of whole months (i.e.,

lags=-12000,-11900,...,-100,0,100,...,11900,12000). So far I have tried to use the code scorr=crosscorr(T,h,'NumLags',12000), and then scorrred=scorr(1:100:24001) but it requires a lot of computation time due to the large number of lags. Is there a way to calculate cross-correlation for non-consecutive lags (i.e. lags=-12000,-11900,...,-100,0,100,...,11900,12000) thus optimizing the time required?

Thank you very much in advance

Answer 1

[Abhimenyu]

Hi Rodrigo,

I understand that you want to calculate cross-correlation for non-consecutive lags and optimize the time required. This can be done by directly calculating the cross-correlation for the specific lags of interest. Since the “crosscorr” function in MATLAB does not inherently support non-consecutive lags, the cross-correlation for the specified lags can be manually calculated.

Please follow the example code below as a suggested approach to calculate the cross-correlation for non-consecutive lags:

% Define the lags of interest 
lagsOfInterest = -12000:100:12000; 

% Pre-allocate array to store cross-correlation values 
crossCorrelationValues = zeros(size(lagsOfInterest)); 

% Get the length of the vectors T and h 
n = length(T); 

% Calculate the cross-correlation for each lag of interest 
for i = 1:length(lagsOfInterest) 
    lag = lagsOfInterest(i); 
    % Calculate the cross-correlation for the current lag 
    if lag < 0 
        crossCorrelationValues(i) = T(1:end+lag) .* h(1-lag:end); 
    else 
        crossCorrelationValues(i) = T(1+lag:end) .* h(1:end-lag); 
    end 
end 

% Normalize the cross-correlation values by the autocorrelations at zero lag 
crossCorrelationValues = crossCorrelationValues / sqrt(corrcoef(T,T) * corrcoef(h,h)); 

The “lagsOfInterest” in the above code contains the specific lags to calculate the cross-correlation. The array, “crossCorrelationValues” is pre-allocated to store the cross-correlation values for each lag. Using a loop, the cross-correlation for each lag can be calculated by summing the products of the appropriately lagged elements of “T” and “h”. Normalizing will help to achieve results very similar to the “crosscorr” function results.

This approach avoids the need to calculate the cross-correlation for all lags and should significantly optimize the computation time for the specific requirements.

I hope this helps to resolve the query.

Thanks,

Abhimenyu