  Probabilistic time series forecasting involves estimating the distribution of
future based on its history, which is essential for risk management in
downstream decision-making. We propose a deep state space model for
probabilistic time series forecasting whereby the non-linear emission model and
transition model are parameterized by networks and the dependency is modeled by
recurrent neural nets. We take the automatic relevance determination (ARD) view
and devise a network to exploit the exogenous variables in addition to time
series. In particular, our ARD network can incorporate the uncertainty of the
exogenous variables and eventually helps identify useful exogenous variables
and suppress those irrelevant for forecasting. The distribution of multi-step
ahead forecasts are approximated by Monte Carlo simulation. We show in
experiments that our model produces accurate and sharp probabilistic forecasts.
The estimated uncertainty of our forecasting also realistically increases over
time, in a spontaneous manner.
