Probabilistic forecasting

So far, we have been talking about the forecast as a single number. We have been projecting our DL models to a single dimension and training the model using a loss such as mean squared loss. This paradigm is what we call a point forecast. A probabilistic forecast is when the forecast, instead of having a single-point prediction, captures the uncertainty of that forecast as well. This means that the model doesn’t output a single number, but an output that reflects the probabilities associated with all possible future outcomes.

In the econometrics and classical time series world, the prediction intervals were already baked into the formulation. The statistical grounding of those methods made sure that the output of those models was readily interpreted in a probabilistic way as well (so long as you could satisfy the assumptions that were stipulated by those models). But in the modern machine/DL world, probabilistic forecasting is not an afterthought...