On studying relations between time series in climatology

Abstract

Abstract. In climatology, relationships between time series are often studied on the basis of crosscorrelation coefficients and regression equations. This approach is generally incorrect for time series irrespective of the crosscorrelation coefficient value because relations between time series are frequency-dependent. Multivariate time series should be analyzed in both time and frequency domains, including fitting a parametric (preferably, autoregressive) stochastic difference equation to the time series and then calculating functions of frequency such as spectra and coherent spectra, coherences, and frequency response functions. The example with a bivariate time series "Atlantic Multidecadal Oscillation (AMO) – sea surface temperature in Niño area 3.4 (SST3.4)" proves that even when the crosscorrelation is low, the time series' components can be closely related to each other. A full time and frequency domain description of this bivariate time series is given. The AMO − SST3.4 time series is shown to form a closed feedback loop system. The coherence between AMO and SST3.4 is statistically significant at intermediate frequencies where the coherent spectra amount up to 55% of the total spectral densities. The gain factors are also described. Some recommendations are offered regarding time series analysis in climatology.