C2FAR: Coarse-to-Fine Autoregressive Networks for Precise Probabilistic Forecasting
Authors: Shane Bergsma, Tim Zeyl, Javad Rahimipour Anaraki, Lei Guo

We present coarse-to-fine autoregressive networks (C2FAR), a method for modeling the probability distribution of univariate, numeric random variables.  C2FAR generates a hierarchical, coarse-to-fine discretization of a variable autoregressively; progressively finer intervals of support are generated from a sequence of binned distributions, where each distribution is conditioned on previously-generated coarser intervals.  Unlike prior (flat) binned distributions, C2FAR can represent values with exponentially higher precision, for only a linear increase in complexity.  We use C2FAR for probabilistic forecasting via a recurrent neural network, thus modeling time series autoregressively in both space and time.  C2FAR is the first method to simultaneously handle discrete and continuous series of arbitrary scale and distribution shape.  This flexibility enables a variety of time series use cases, including anomaly detection, interpolation, and compression.  C2FAR achieves improvements over the state-of-the-art on several benchmark forecasting datasets.