I have a data set including 25 variables $(x_{1,t},\dotsc,x_{25,t})$ at each time $t$ and all of this group is repeated through time. I want to explore the relationship between these variables through time and for example say that $x_{1,t}$ is highly correlated with $x_{t,10}$ during lapsed time. Then summarize the number of variables so that those which are more crucial and important be selected.
I am not looking for forecasting but I just to find out which variables are highly correlated and then decrease the number of variables.
I have read about factor analysis but I think it is not applicable for time series data.