I have a multivariate problem (with solar data from different meteorological stations) that I am working on my engineering master thesis. I would like to estimate the correlations of different variables pairs. However I would also like to know if the values from the sample time (monthly data for some 20 years) is representative of the real values. The question involves how can I calculate confidence interval on such cases.
The two methods I considered was based on fisher transformation and on bootstrapping. However, for both cases I would like to know:
- How can I verify if correlations are time-independent?
- If they are not, how could I apply those methods?
My Idea so far was to calculate correlations for groups of n months (I was thinking in using 6) and see if there was time-dependency by using a test such as Ljung-Box. Than the sample size used on fishers transformation would be the original one divided by n. Using bootstrap, The permutations would be of these groups with n months.
Is my idea fine? How could I make this analysis better?