Data independence is important in many statistical analysis. But how to check the independence of each other. For instance, I have time series data of precipitation (P) and transpiration (T). Could I use the covariance (cov(P, T)) or Pearson correlation coefficient to judge whether they are independent of each other or maybe other more suitable metrics? Thanks in advance.
i would use Fisher's exact test if your variables are categorical or can be categorized. if they are continuous I'd measure mutual information, via their entropies.
Precipitation and transpiration cannot be categorical. Rather they are ratio variables. Pearson's product moment correlation coefficient may be calculated for them. Also a contingency table can be developed for them for which a chi-square statistic can be calculated for them and tested for significance.
You have to use regression analysis in some good time series based data based softwares like E-Views.
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