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I have a question about the applicability of the Hilbert-Huang Transform / empirical mode decomposition (HHT/EMD).

Suppose I have a time series dataset in which there is probably an N-year periodic component, some shorter-period periodic components, a linear trend, and noise. Unfortunately, my dataset is considerably shorter than N years. My goal is not to find the periodic components (though that would be mildly interesting), but to more accurately find the linear trend, by removing the influence of the periodic components.

Is HHT/EMD useful for this? Can it help me make a more accurate determination of the linear trend than simple linear regression analysis would do?

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Well, I am new to HHT, having recently tried out several different algorithms in Matlab... But since no one has answered your question I will take a stab at providing some information.

HHT, as you know, uses EMD to break the original signal into IMF's, which are oscillatory signals. The first IMF produced contains the highest frequency content, the last imf contains the lowest frequency content. To be a valid IMF the number of zero crossings has to be close to the number of oscillations extrema (within ~1). The Hilbert transform is applied to each IMF to determine the instantaneous amplitude, phase, and frequency of the oscillating signal.

I bring this up because if you suspect the period is N years, but your data set is less than N years... then the N period content might not be oscillatory and/or the number of extrema and zero crossings might be too different... the EMD might not be able to extract out a valid IMF for the N year periodicity that is distinct from the linear trend.

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