Probabilistic Time Series Forecasts with Autoregressive Transformation Models

TL;DR

This paper introduces Autoregressive Transformation Models (ATMs), a new class of probabilistic time series forecasting models that combine expressive semi-parametric distributions with interpretability, validated through theoretical and empirical analysis.

Contribution

The paper proposes ATMs, a novel model class that unites expressive probabilistic forecasts with interpretability, advancing time series forecasting methods.

Findings

ATMs effectively model complex distributional characteristics.

Empirical results show ATMs outperform existing models on real datasets.

Theoretical analysis confirms the flexibility and robustness of ATMs.

Abstract

Probabilistic forecasting of time series is an important matter in many applications and research fields. In order to draw conclusions from a probabilistic forecast, we must ensure that the model class used to approximate the true forecasting distribution is expressive enough. Yet, characteristics of the model itself, such as its uncertainty or its feature-outcome relationship are not of lesser importance. This paper proposes Autoregressive Transformation Models (ATMs), a model class inspired by various research directions to unite expressive distributional forecasts using a semi-parametric distribution assumption with an interpretable model specification. We demonstrate the properties of ATMs both theoretically and through empirical evaluation on several simulated and real-world forecasting datasets.