Abstract
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.
Highlights
Time series analysis finds applications in a wide range of disciplines, from science to engineering and from marketing to econometrics; it naturally plays a critical role in geophysics, meteorology, hydrology, or the exploitation of remote sensing data
The Kondrashov and Ghil method turns out to be more accurate than both Lomb-Scargle algorithms, but the best fit to the original data is produced by the smoothing spline algorithm
Aperiodic components in the signal or a distribution of gaps that interferes with the base frequencies of the signal are likely to cause less reliable results, up to the point of generating spurious, intermittent fluctuations in the reconstructed signal that were never present in the original data
Summary
Time series analysis finds applications in a wide range of disciplines, from science to engineering and from marketing to econometrics; it naturally plays a critical role in geophysics, meteorology, hydrology, or the exploitation of remote sensing data. A time series is a finite, ordered set of couples of numerical expressions {(ti,xi);i = 0,1,...,n}, one providing a time reference and the other corresponding to the value of a measurement or observation acquired at that time. One might be interested in determining the likely value of the variable of interest at a time that may not coincide with a particular measurement or observation. For these reasons, it is useful to be able to generate reasonable estimates of the values of the variable of interest for arbitrary time references, including to replace missing values
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