A non-parametric method to test the statistical significance in rolling window correlations, and applications to ecological time series

We provide a non-parametric computing-intensive method to test the statistical significance of the rolling window correlation for bi-variate time series. This method (test) addresses the effects due to the multiple testing (inflation of the Type I error) when the statistical significance is estimated for the rolling window correlation coefficients. We follow Telford and Polanco-Martinez to carry out the proposed method. The method is based on Monte Carlo simulations by permuting one of the variables (dependent) under analysis and keeping fixed the other variable (independent). We improve the computational time of this method to reduce the computation time (speedup was up to practically five times faster than the sequential method using 11 cores) through parallel computing. We compare the results obtained through the proposed method with two p-value correction methods frequently used (Bonferroni and Benjamini and Hochberg -BH) after being applied to synthetic and to real-life ecological time series. Our results show that the proposed method works roughly similar to these two p-value correction methods, especially with the method of BH, but our test is a little more restrictive than BH and a little more permissive than Bonferroni. The test is programmed in R and is included in the package NonParRolCor that is available freely on CRAN.