Selection of the Parameter of the Synchrony Estimator for the Correlation Between Time Series Sampled at Different Time Points

Abstract The synchrony estimator with parameter $$\beta $$ β for the correlation between two time series observed at different time points is defined as the standard Pearson correlation coefficient computed using a fraction $$\beta $$ β of the pairs of the two series corresponding to the smallest time differences. Two problems limit the use of the estimator in applications. First, no rule is available for selecting $$\beta $$ β . Second, it has been argued in the literature that the estimator only partially exploits the information in the data, since it does not use all available observations. In this paper, we address these issues under the assumption that the data-generating process is a bivariate first-order autoregressive [AR(1)] model with positive autocorrelation coefficients. This assumption follows from embedding and identifiability considerations and the widespread use of AR(1) models in geoscience applications. The main contribution is an algorithm for selecting the $$\beta $$ β parameter of the synchrony estimator. We illustrate the performance of the proposed procedure using simulated data. We found evidence that, contrary to what has been claimed in the literature, not using all available observations individually is a strength of the synchrony estimator rather than a weakness. As such, the synchrony estimator is a valid option for estimating the correlation. The proposed procedure is also extended to the selection of the $$\beta $$ β parameter of the synchrony estimator of the cross-correlation function. Relevant aspects of its implementation are presented and illustrated with examples using simulated and real climatological data.