  Probabilistic time series forecasting has played critical role in
decision-making processes due to its capability to quantify uncertainties. Deep
forecasting models, however, could be prone to input perturbations, and the
notion of such perturbations, together with that of robustness, has not even
been completely established in the regime of probabilistic forecasting. In this
work, we propose a framework for robust probabilistic time series forecasting.
First, we generalize the concept of adversarial input perturbations, based on
which we formulate the concept of robustness in terms of bounded Wasserstein
deviation. Then we extend the randomized smoothing technique to attain robust
probabilistic forecasters with theoretical robustness certificates against
certain classes of adversarial perturbations. Lastly, extensive experiments
demonstrate that our methods are empirically effective in enhancing the
forecast quality under additive adversarial attacks and forecast consistency
under supplement of noisy observations.
