  A Recurrent Neural Network that operates on several time lags, called an
RNN(p), is the natural generalization of an Autoregressive ARX(p) model. It is
a powerful forecasting tool when different time scales can influence a given
phenomenon, as it happens in the energy sector where hourly, daily, weekly and
yearly interactions coexist. The cost-effective BPTT is the industry standard
as learning algorithm for RNNs. We prove that, when training RNN(p) models,
other learning algorithms turn out to be much more efficient in terms of both
time and space complexity. We also introduce a new learning algorithm, the Tree
Recombined Recurrent Learning, that leverages on a tree representation of the
unrolled network and appears to be even more effective. We present an
application of RNN(p) models for power consumption forecasting on the hourly
scale: experimental results demonstrate the efficiency of the proposed
algorithm and the excellent predictive accuracy achieved by the selected model
both in point and in probabilistic forecasting of the energy consumption.
