The ordinary test of significance of the correlation coefficient assumes that successive observations are independent. This assumption is often not fulfilled in time series. If either of the 2 series correlated is random the usual test is valid; otherwise it will admit as significant correlations that should not be. It is unwise to fit trends of too high order. If a series is complicated, it is better to split it into parts and fit trends to each part separately. The variate difference method is rather inefficient.