How to predict with EMD? Because the EMD algorithm decomposes time series into a number of periodics of different frequency (IMFs), and a residue trend, prediction in EMD is by extrapolating each of the IMFs separately (a VAR model is recommended) and fitting a cubic polynomial to the residue (example code at end of here). The predictions are then added together.
Below are a couple of examples of EMD predictions on familiar data sets, the HadCRU global surface temperature, and the TLT series from the satellite MSU RSS data. In both I have also applied the recommended prediction techniques to extend the result into the future.
The first is the satellite TLT, and I have used up to IMF 5 so that variation up to annual quasi-periodicity is represented. The residue in this case, the red arch, has peaked and is projected to decline, along with the overall temperature, in the next few years. The amplitude of variability is also declining.
Below is the result for CRU, and I have used IMF’s up to the 11 year solar cycle (including the 22 year IMF and the ~60 year cycle). The residue trend is increasing (global warming has not stopped!), although the rate of increase is at the extreme low end of IPCC projections. The pop up predicted for the next few years seems to presume another strong solar cycle (referring to the individual IMF’s). If this doesn’t eventuate, as it looks like it won’t, one could omit the 11 and 22 year cycles, and simply use the 60 year and residue for prediction.
The periodic IMF’s are also plotted along the zero line, to show the degree of variation associated with natural variation.
The paper by Wu et al On the trend, detrending, and variability of nonlinear and nonstationary time series is well worth a read. It introduces EMD as a contender for optimal smoothing of climate series. Climate science should be looking for one after the poster child of global warming was demolished here, and here at ClimateAudit, and ‘worse than we thought’ alarmism abuse of it was exposed here.
After EMD extracts sequentially the frequency modes, Wu claims the residue is ‘intrinsic’ to the data, and not ‘extrinsic’ as a predetermined shape, like a straight line, and unlike a moving average it extends to the end without blowing out the confidence intervals. The approach certainly would seem to handle the end-point problem better than ‘end-pinning’ or other pathological methods used often in climate science (but only when the end points are high!). The benefit of being ‘intrinsic’ is that the resulting trend is more objective. The definition of trend in EMD is more generic than most, usually being monotonic increasing, but the residue can be S shaped too. It is always a concern if the method introduces biases, and I am not convinced that EMD does not equally contain biases, they are just hidden deeper in the guts of the algorithm for extracting out the IMF’s.