# C2FAR: Coarse-to-Fine Autoregressive Networks for Precise Probabilistic Forecasting

Source: [C2FAR: Coarse-to-Fine Autoregressive Networks for Precise Probabilistic Forecasting](<https://www.sota2.com/research/paper/68fa71ac1e209131cea527a5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-01-02T04:38:13.139Z

Authors: Shane Bergsma, Timothy Zeyl, Javad Rahimipour Anaraki, Lei Guo

Published: 2023-12-22T16:37:52.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Probabilistic Forecasting on elec](<https://www.sota2.com/research/sota/probabilistic-forecasting-on-elec.md>): Probabilistic Forecasting; Elec; ND%: 6.

- [Probabilistic Forecasting on traff](<https://www.sota2.com/research/sota/probabilistic-forecasting-on-traff.md>): Probabilistic Forecasting; traff; ND%: 12.9.

- [Probabilistic Forecasting on azure](<https://www.sota2.com/research/sota/probabilistic-forecasting-on-azure.md>): Probabilistic Forecasting; azure; ND (%): 2.77.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2312.15002>)

[PDF](<https://arxiv.org/pdf/2312.15002.pdf>)

[Implementation](<https://github.com/huaweicloud/c2far_forecasting>)