  This work studies the threats of adversarial attack on multivariate
probabilistic forecasting models and viable defense mechanisms. Our studies
discover a new attack pattern that negatively impact the forecasting of a
target time series via making strategic, sparse (imperceptible) modifications
to the past observations of a small number of other time series. To mitigate
the impact of such attack, we have developed two defense strategies. First, we
extend a previously developed randomized smoothing technique in classification
to multivariate forecasting scenarios. Second, we develop an adversarial
training algorithm that learns to create adversarial examples and at the same
time optimizes the forecasting model to improve its robustness against such
adversarial simulation. Extensive experiments on real-world datasets confirm
that our attack schemes are powerful and our defense algorithms are more
effective compared with baseline defense mechanisms.
