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.