Non-parametric Probabilistic Time Series Forecasting via Innovations
  Representation
Xinyi Wang Meijen Lee Qing Zhao Lang Tong
Probabilistic time series forecasting predicts the conditional probability
distributions of the time series at a future time given past realizations. Such
techniques are critical in risk-based decision-making and planning under
uncertainties. Existing approaches are primarily based on parametric or
semi-parametric time-series models that are restrictive, difficult to validate,
and challenging to adapt to varying conditions. This paper proposes a
nonparametric method based on the classic notion of {\em innovations} pioneered
by Norbert Wiener and Gopinath Kallianpur that causally transforms a
nonparametric random process to an independent and identical uniformly
distributed {\em innovations process}. We present a machine-learning
architecture and a learning algorithm that circumvent two limitations of the
original Wiener-Kallianpur innovations representation: (i) the need for known
probability distributions of the time series and (ii) the existence of a causal
decoder that reproduces the original time series from the innovations
representation. We develop a deep-learning approach and a Monte Carlo sampling
technique to obtain a generative model for the predicted conditional
probability distribution of the time series based on a weak notion of
Wiener-Kallianpur innovations representation. The efficacy of the proposed
probabilistic forecasting technique is demonstrated on a variety of electricity
price datasets, showing marked improvement over leading benchmarks of
probabilistic forecasting techniques.