Empirical mode decomposition using rational splines: an application to rainfall time series

Abstract

Empirical mode decomposition (EMD), a relatively new form of time-series decomposition, has the feature of not assuming that a time series is linear or stationary, as is implicitly done in Fourier analysis. In natural time series such as records of rainfall, streamflow, temperature, etc., where most variables exhibit nonlinear and non-stationary behaviour, this feature is particularly useful, allowing more meaningful quantification of the proportion of variance in a time series due to fluctuations at different time scales, than previous spectral analysis techniques. However, in its original form, the EMD algorithm relies on cubic spline interpolation of the extrema, which often inflate the variance of the resultant components (intrinsic mode functions) and residual. In this paper, a suggested improvement to the EMD algorithm, using rational splines and flexible treatment of the end conditions, is outlined and the consequent effect on three exemplary annual rainfall time series is assessed as a proof of concept. It is recognized that many more examples are needed for the fine tuning of the ideas before it can be widely recommended and this work is currently underway.