C2FAR: Coarse-to-Fine Autoregressive Networks for Precise Probabilistic
  Forecasting
Shane Bergsma Timothy 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.