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There is a vast literature on modelling time-series with periodcities. Rob Hyndman is one of the leading reseaerchers in this area. He has published the R package forecast and a free online text book on this subject (with another package and R code in the book). Your task is covered starting here.


Looking for the same issue, I found an article by de Jong(1997). In section 2 you can find a method for estimation of covariances and correlations between irregularly spaced data. Also look at the article by Jonas Andersson where some interpolation methods and method form de Jong are presented and compared together. Hope it helps.

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