Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows

TL;DR

This paper introduces a novel autoregressive deep learning model using conditioned normalizing flows to effectively model high-dimensional multivariate time series, improving forecasting accuracy over existing methods.

Contribution

It combines autoregressive models with conditioned normalizing flows to better capture dependencies in high-dimensional multivariate time series data.

Findings

Outperforms state-of-the-art methods on real-world datasets

Handles thousands of interacting time series efficiently

Maintains computational tractability with high-dimensional data

Abstract

Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting time series. However, modeling statistical dependencies can improve accuracy and enable analysis of interaction effects. Deep learning methods are well suited for this problem, but multivariate models often assume a simple parametric distribution and do not scale to high dimensions. In this work we model the multivariate temporal dynamics of time series via an autoregressive deep learning model, where the data distribution is represented by a conditioned normalizing flow. This combination retains the power of autoregressive models, such as good performance in extrapolation into the future, with the flexibility of flows as a general purpose high-dimensional distribution model, while remaining computationally tractable. We show that it improves over the state-of-the-art for standard metrics on many real-world data sets with several thousand interacting time-series.