Estimating Pearson's Correlation Coefficient with Bootstrap Confidence Interval from Serially Dependent Time Series

Abstract

Pearson's correlation coefficient, rxy, is often used when measuring the influence of one time-dependent variable on another in bivariate climate time series. Thereby, positive serial dependence (persistence) and unknown data distributions impose a challenge for obtaining accurate confidence intervals for rxy. This is met by the presented approach, employing the nonparametric stationary bootstrap with an average block length proportional to the maximum estimated persistence time of the data. A Monte Carlo experiment reveals that this method can produce accurate (in terms of coverage) confidence intervals (of type bias-corrected and accelerated). However, since persistence reduces the number of independent observations, substantially more data points are required for achieving an accuracy comparable to a situation without persistence. The experiment further shows that neglecting serial dependence may lead to serious coverage errors. The presented method proves robust with respect to distributional shape (lognormal/normal) and time spacing (uneven/even). The method is used to confirm that a previous finding of a correlation between solar activity and Indian Ocean monsoon strength in early Holocene is valid. A further result is that the correlation between sunspot number and cosmogenic 10Be concentration vanishes after approximately 1870.