Online Time Series Forecasting with Theoretical Guarantees

TL;DR

This paper introduces a theoretical framework for online time series forecasting that accounts for distribution shifts and latent variables, providing guarantees and practical algorithms that improve forecasting accuracy.

Contribution

It develops a novel theoretical framework with guarantees for online forecasting involving latent variables and proposes a model-agnostic blueprint with practical implementations.

Findings

Theoretical guarantees tighten Bayes risk with latent variables.

Latent variables identification improves forecasting under distribution shifts.

Experimental results show consistent improvements on synthetic and real-world data.

Abstract

This paper is concerned with online time series forecasting, where unknown distribution shifts occur over time, i.e., latent variables influence the mapping from historical to future observations. To develop an automated way of online time series forecasting, we propose a Theoretical framework for Online Time-series forecasting (TOT in short) with theoretical guarantees. Specifically, we prove that supplying a forecaster with latent variables tightens the Bayes risk, the benefit endures under estimation uncertainty of latent variables and grows as the latent variables achieve a more precise identifiability. To better introduce latent variables into online forecasting algorithms, we further propose to identify latent variables with minimal adjacent observations. Based on these results, we devise a model-agnostic blueprint by employing a temporal decoder to match the distribution of observed variables and two independent noise estimators to model the causal inference of latent variables and mixing procedures of observed variables, respectively. Experiment results on synthetic data support our theoretical claims. Moreover, plug-in implementations built on several baselines yield general improvement across multiple benchmarks, highlighting the effectiveness in real-world applications.