Below are the results of applying the EMD algorithm (Empirical Mode Decomposition) to Australian Rainfall, and predicting the future rainfall with a VAR model (Vector Autoregression).
First, EMD splits the rainfall into IMF’s (Intrinsic Mode Functions) that are cyclical but variable in amplitude and frequency.
You can see each of the modes, their strength and phase, and the uncertainty. The initial modes are very uncertain, not worth including in the model, so only a few IMF are used in the fit and prediction below.
You can see the drought conditions prevailing in the last few years, and the strong rebound in precipitation predicted from the model. Note the uncertainty limits expand very quickly, indicating that only a decade or so ahead is predictable before errors in each of the IMF’s overwhelms. See Demetris’s excellent paper on this for more information.
This model has a Nash-Sutcliffe Efficiency of around 0.1, better than the mean value, but not huge. Another way to evaluate it is to do the prediction to a specific date, leaving out some data. The following was done to 1980.
Clearly there is some skill at predicting peaks, but should not be relied on at this stage.
I am still working on the code for this, and will post it shortly, but I call it with a function:
The Ar is the time series for the rainfall, stationary=T lets me exclude any trend from the model (as trends in rainfall are very uncertain), N is the number of IMF’s to use, and end=1990 is where the data is used to.