I Is there a better way to calculate time-shifted correlation matrices?

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The discussion focuses on calculating time-shifted correlation matrices for temperature data collected from four thermometers. The initial method involves removing specific rows from the data matrix to analyze changes in correlation. The author seeks alternative approaches to this row-removal technique. Python's numpy library is utilized for calculating both shifted and non-shifted correlation matrices. The conversation highlights a need for methods that address cross-sensor delayed correlations rather than just autocorrelations.
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I want to know if there is a better way to obtain the correlation matrix of time-shifted series than just removing observations.
Hello everyone.

I have four thermometers which measure the temperature in four different positions. The data is distributed as a matrix, where each column is a sensor, and each row is a measurement. All measurements are made at exactly the same times, one measurement each hour. I have calculated the correlation matrix between all four positions.

Now I am interested in the calculation of the time-shifted correlation matrix. The only method I can think of is to remove the first n rows of the sensors 1 and 2 and the last n rows of the sensors 3 and 4 to see how the correlation changes.

I was wondering if there is a better way to do this than just removing rows.

Any help is appreciated.

Best regards.
Frank.

PS. I am using Python, so I have just used the function np.cov(Tdata_shifted2) and np.cov(Tdata) to obtain the shifted an non-shifted matrices.
 
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This stackexchange problem seems to match yours.
Most answers seem to only address calculating autocorrelations of each sensor with itself, not cross-sensor delayed correlations. It looks like you do want those latter. The answer by jboi (Feb 17, 2018 at 22:38) seems to provide those.
 
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Thanks for the answer
 
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