  This paper proposes a nonparametric multivariate density forecast model based
on deep learning. It not only offers the whole marginal distribution of each
random variable in forecasting targets, but also reveals the future correlation
between them. Differing from existing multivariate density forecast models, the
proposed method requires no a priori hypotheses on the forecasted joint
probability distribution of forecasting targets. In addition, based on the
universal approximation capability of neural networks, the real joint
cumulative distribution functions of forecasting targets are well-approximated
by a special positive-weighted deep neural network in the proposed method.
Numerical tests from different scenarios were implemented under a comprehensive
verification framework for evaluation, including the very short-term forecast
of the wind speed, wind power, and the day-ahead forecast of the aggregated
electricity load. Testing results corroborate the superiority of the proposed
method over current multivariate density forecast models considering the
accordance with reality, prediction interval width, and correlations between
different random variables.
