  Multi-variate time series forecasting is an important problem with a wide
range of applications. Recent works model the relations between time-series as
graphs and have shown that propagating information over the relation graph can
improve time series forecasting. However, in many cases, relational information
is not available or is noisy and reliable. Moreover, most works ignore the
underlying uncertainty of time-series both for structure learning and deriving
the forecasts resulting in the structure not capturing the uncertainty
resulting in forecast distributions with poor uncertainty estimates. We tackle
this challenge and introduce STOIC, that leverages stochastic correlations
between time-series to learn underlying structure between time-series and to
provide well-calibrated and accurate forecasts. Over a wide-range of benchmark
datasets STOIC provides around 16% more accurate and 14% better-calibrated
forecasts.
  STOIC also shows better adaptation to noise in data during inference and
captures important and useful relational information in various benchmarks.
