Robust detection of statistically significant correlations in geophysical timeseries: A Monte Carlo method accounting for serial dependence and sampling uncertainty
2021
Two geophysical timeseries may share a common low-frequency signal that is distorted by high-frequency noise.As such, these timeseries are often filtered to remove the high-frequency noise prior to performing statistical analysis.However, this filtering artificially increases the serial dependence of the timeseries, meaning that the assumption of independent data underlying most standard correlation tests (e.g.Pearson's correlation) is violated.Monte Carlo methods that account for serial dependence when comparing serially dependent data are typically focused on either (a) calculating the p-value of the observed correlation with respect to an empirically derived null distribution, which is derived by calculating the correlation between independently generated replicates of the observed data or (b) estimating sampling uncertainty in the observed statistic by performing a block bootstrap, with block size proportional to the serial dependence in the timeseries.In this study, we present a Monte Carlo test that combines these two approaches and, in doing so, explicitly accounts for serial dependence and sampling uncertainty when comparing two timeseries.A case study is presented that demonstrates the ability of the proposed method to detect statistically insignificant correlations when performed on filtered white noise timeseries.Crucially, existing methods accounting for serial dependence detected a statistically significant, spurious correlation.This demonstrates that the proposed method is suitable for use when performing statistical analysis on filtered timeseries.