Comparing methods for analysing time scale dependent correlations in irregularly sampled time series data

Time series derived from paleoclimate archives are often irregularly sampled in time and thus not analysable using standard statistical methods such as correlation analyses. Although measures for the similarity between time series have been proposed for irregular time series, they do not account for the time scale dependency of the relationship. Stochastically distributed temporal sampling irregularities act qualitatively as a low-pass filter reducing the influence of fast variations from frequencies higher than about 0.5 (Δtmax) − 1, where Δtmax is the maximum time interval between observations. This may lead to overestimated correlations if the true correlation increases with time scale. Typically, correlations are underestimated due to a non-simultaneous sampling of time series. Here, we investigated different techniques to estimate time scale dependent correlations of weakly irregularly sampled time series, with a particular focus on different resampling methods and filters of varying complexity. The methods were tested on ensembles of synthetic time series that mimic the characteristics of Holocene marine sediment temperature proxy records. We found that a linear interpolation of the irregular time series onto a regular grid, followed by a simple Gaussian filter was the best approach to deal with the irregularity and account for the time scale dependence. This approach had both, minimal filter artefacts, particularly on short time scales, and a minimal loss of information due to filter length