Empirical Mode Decomposition for Analyzing Nonstationary Trading Data
Summary
The article introduces empirical mode decomposition (EMD) as a way to break a complex time series into oscillatory components called intrinsic mode functions, plus a residual. Unlike Fourier and wavelet methods that use a selected basis, EMD derives its components adaptively from the input sequence. The discussion defines the conditions an intrinsic mode function should satisfy and explains that successive components generally represent progressively lower-frequency behavior.
The method repeatedly finds local maxima and minima, fits upper and lower envelopes with cubic splines, subtracts their mean, and sifts the result until a stopping condition is reached. Extracted components are removed in sequence until the remaining residual has few extrema. The article outlines a software implementation and examples, but warns that stopping criteria affect results, the implementation may need further improvement, and derived components should not be treated as the original physical causes of the data. The Hilbert transform stage of the broader Hilbert–Huang method is outside its main scope.
Key ideas
- EMD builds an adaptive decomposition basis from the observed sequence rather than a fixed analytic basis.
- Intrinsic mode functions meet constraints on extrema, zero crossings, and local envelope means.
- Sifting repeatedly subtracts the mean of spline envelopes fitted through local maxima and minima.
- Stopping criteria influence the resulting decomposition, and implementation choices can affect interpretation.
- EMD components are analytical constructs and do not necessarily correspond to actual market-generating processes.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.