There is a question of utmost importance when it comes to statistical forecasting: what is error function used during the learning process? Indeed, it’s based on the error function that you can evaluate whether a forecast is good or bad. It’s also the very same error function that drives your learning process when building a statistical model.
Finding an error function isn’t hard. Quite the opposite, there are plenty of error functions available: Mean Squared Error (MSE), Mean Absolute Deviation, Median Absolute Deviation Error (MAD), Mean Absolute Percentage Error (MAPE). …
Yet, in almost 1 year of existence for Lokad, the question of the choice of error function has never been raised by any customer. Well, this situation is very natural, as Lokad is precisely taking in charge the whole forecasting process.
For those who might be interested, the answer is, unfortunately, not simple. Lokad using several error functions depending on the context. We are often using bounded version of the MAPE (identical to the classical MAPE, but the function gets upper bounded to 1) for the benchmarks. The upper bound is used to make the process more robust against pathological time-series that would have had huge errors otherwise.
Yet, if the data is not too noisy (i.e. not too much outliers), then we are often using the MSE function which tends to be much more practical from a computational viewpoint.