Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting

TL;DR

This paper introduces TimeGrad, an autoregressive diffusion model for multivariate probabilistic time series forecasting that outperforms existing methods on real-world datasets with high-dimensional data.

Contribution

The paper presents a novel autoregressive diffusion approach for probabilistic forecasting, leveraging score matching and Langevin sampling, achieving state-of-the-art results.

Findings

Outperforms existing methods on real-world datasets

Handles thousands of correlated dimensions effectively

Provides a new foundation for future research in probabilistic time series forecasting

Abstract

In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion probabilistic models, a class of latent variable models closely connected to score matching and energy-based methods. Our model learns gradients by optimizing a variational bound on the data likelihood and at inference time converts white noise into a sample of the distribution of interest through a Markov chain using Langevin sampling. We demonstrate experimentally that the proposed autoregressive denoising diffusion model is the new state-of-the-art multivariate probabilistic forecasting method on real-world data sets with thousands of correlated dimensions. We hope that this method is a useful tool for practitioners and lays the foundation for future research in this area.