Suppose I see that there are 3 series X,Y and Z all of which granger cause another series A. Is there any way to check which one among X,Y and Z are most useful to forecast A?
If a process has multiple causal variables rank these variables according to the decreasing order of their specific gravity which is the inverse of MFPE (multivariate final prediction error)
You should specify three regression models, with either X, Y or Z on the right hand side. Produce ex post out-of-sample forecasts for A for the desired forecasting horizon against a benchmark (for instance autoregressive model) and compare the root mean squared (or mean absolute) errors. The significance of the differences in the forecast accuracy can be investigated by various tests, including the Diebold-Mariano test. Look at the root mean squared forecast errors to decide, whether X, Y or Z is more useful for your task. The choice will be on the variable with the lowest root mean squared (mean absolute) forecast error relative to the benchmark.
Keep in mind that Granger causality is an in-sample concept, i.e. based on the in-sample fit of a regression. This does not imply anything on the forecasting performance in an out of sample exercise (which mimics the situation where the forecaster is actually in). So, probably, you should forecast A by a combination of X, Y and Z. This might deliver even more accurate forecasts than the best individual variable, be it X, Y or Z.
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