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

Abstract

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 (∆ $%&) () , where ∆ $%& 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.

Estimating the timescale-dependent uncertainty of paleoclimate records – a spectral approach. Part II: Application and interpretation

“…We estimated the timescale dependent correlation between Rep1 and Rep2 using the R package corit (Reschke et al, 2019).…”

Changes in the composition of marine and sea-ice diatoms derived from sedimentary ancient DNA of the eastern Fram Strait over the past 30 000 years

“…All statistical analyses and visualisations were prepared with R v. 3.5.0 using the packages "vegan" (Oksanen et al, 2011) and "rioja" (Juggins, 2012). For correlation analysis we interpolated IP 25 values using the methods described in Reschke et al (2019). We transformed the IP 25 data using the function zoo from the "zoo" package (Zeileis and Grothendieck, 2005) and used the function CorIr-regTimser using the package "corit" (https://github.com/ EarthSystemDiagnostics/corit, last access: 2 March 2020) (Reschke et al, 2019).…”

“…For correlation analysis we interpolated IP 25 values using the methods described in Reschke et al (2019). We transformed the IP 25 data using the function zoo from the "zoo" package (Zeileis and Grothendieck, 2005) and used the function CorIr-regTimser using the package "corit" (https://github.com/ EarthSystemDiagnostics/corit, last access: 2 March 2020) (Reschke et al, 2019). The correlation between Chaetocero-taceae and Thalassiosiraceae as well as between IP 25 and all ASVs was tested for significance using the R function rcorr (method Pearson) from the package "Hmisc" (Hollander and Wolfe, 1975;Press et al, 1988).…”

Testing the consistency of Holocene and Last Glacial Maximum spatial correlations in temperature proxy records

“…Shaded areas depict the area of ±σ (standard deviation) of the correlation decay length estimates for the latitudes. [Color figure can be viewed at wileyonlinelibrary.com] (power spectrum) of the climate signal (rapidly varying signals are more susceptible to time uncertainty); and (iv) the timescale on which the correlation is estimated if the noise and the climate signal components have different temporal structures (Reschke et al, 2019b).…”