The sensitivity of the empirical mode decomposition and its application on environmental data

Abstract

The Empirical Mode Decomposition (EMD) is a powerful data analysis method that can be used to extract embedded components within time series and other data. In the context of EMD, these embedded components are called Intrinsic Mode Functions (IMF). Since its inception in the late 1990s, EMD has been applied in a number of areas, including biomedicine, neuroscience, epidemiology, chemical engineering, finance, atmospheric turbulence, seismology and oceanography. The method is advantageous in that it is able to analyse nonlinear and non-stationary data. Surprisingly, the literature exploring the ability of EMD to analyse data with different types of non-stationarity is relatively sparse. Also, the sensitivities associated with the critical initial steps of the EMD procedure are not well understood. One of the critical steps in determining each of the IMFs involves constructing upper and lower envelopes of the local maxima and minima of the time series. In the original presentation of the EMD methodology, cubic-spline interpolation was used to construct these envelopes. However, there is no a priori reason to support the use of cubic splines, and it is natural to wonder how employing alternative interpolation methods might affect the ultimate outcome of the EMD method. This dissertation is dedicated to providing a more comprehensive understanding of the sensitivity of EMD to different interpolation methodologies, and to different types of data non-stationarity. These sensitivities are investigated systematically using synthetic time series data that cover a range of interesting features. In addition, a number of environmental data sets are used to explore how EMD sensitivity can inffuence the inferences that might be drawn from IMFs extracted using various forms of the EMD method. In this part of the study, temperature, sea level and forest fire danger rating time series are chosen. There is significant interest in the way these particular variables might be changing over various time scales, and how these changes might impact various ecosystems, including human societies. The analyses conducted in this thesis suggest that the robustness and accuracy of EMD is improved when smoothing-spline interpolation is employed as its underlying interpolation method. In particular, Smoothing Ensemble EMD (SEEMD) is introduced, and is shown to out-perform other EMD methods in a number of important contexts. Specifically, SEEMD is shown to be more robust in the presence of noise and is able to extract more meaningful features from the environmental times series. It is also found, however, that all EMD-based methods perform poorly when confronted with time series exhibiting abrupt non-stationarity.