Technical Note: Comparing the effectiveness of recent algorithms to fill and smooth incomplete and noisy time series

Abstract

Geophysical time series often feature missing data or data acquired at irregular times. Procedures are needed to either resample these series at systematic time intervals or to generate reasonable estimates at specified times in order to meet specific user requirements or to facilitate subsequent analyses. Interpolation methods have long been used to address this problem, taking into account the fact that available measurements also include errors of measurement or uncertainties. This paper inspects some of the currently used approaches to fill gaps and smooth time series (smoothing splines, Singular Spectrum Analysis and Lomb-Scargle) by comparing their performance in either reconstructing the original record or in minimizing the Mean Absolute Error (MAE), Mean Bias Error (MBE), chi-squared test statistics and autocorrelation of residuals between the underlying model and the available data, using both artificially-generated series or well-known publicly available records. Some methods make no assumption on the type of variability in the data while others hypothesize the presence of at least some dominant frequencies. It will be seen that each method exhibits advantages and drawbacks, and that the choice of an approach largely depends on the properties of the underlying time series and the objective of the research.