  Some real-world decision-making problems require making probabilistic
forecasts over multiple steps at once. However, methods for probabilistic
forecasting may fail to capture correlations in the underlying time-series that
exist over long time horizons as errors accumulate. One such application is
with resource scheduling under uncertainty in a grid environment, which
requires forecasting electricity demand that is inherently noisy, but often
cyclic. In this paper, we introduce the conditional approximate normalizing
flow (CANF) to make probabilistic multi-step time-series forecasts when
correlations are present over long time horizons. We first demonstrate our
method's efficacy on estimating the density of a toy distribution, finding that
CANF improves the KL divergence by one-third compared to that of a Gaussian
mixture model while still being amenable to explicit conditioning. We then use
a publicly available household electricity consumption dataset to showcase the
effectiveness of CANF on joint probabilistic multi-step forecasting. Empirical
results show that conditional approximate normalizing flows outperform other
methods in terms of multi-step forecast accuracy and lead to up to 10x better
scheduling decisions. Our implementation is available at
https://github.com/sisl/JointDemandForecasting.
