Probabilistic time series forecasts with autoregressive transformation models

Statistics and Computing, vol. 33

Abstract

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.

Authors 4

1. David Rügamer corresponding Aachen Institute of Statistics

   TU Dortmund University · Munich Center for Machine Learning · Ludwig-Maximilians-Universität München · RWTH Aachen University

   Affiliation as printed

   Department of Statistics, LMU Munich, Munich, Germany

   Department of Statistics, TU Dortmund, Dortmund, Germany

   Institute of Statistics, RWTH Aachen, Aachen, Germany

   Munich Center for Machine Learning (MCML), LMU Munich, Munich, Germany

2. Philipp F. M. Baumann

   ETH Zurich

   Affiliation as printed

   KOF Swiss Economic Institute, ETH Zurich, Zurich, Switzerland

3. Thomas Kneib

   University of Göttingen

   Affiliation as printed

   Chair of Statistics, University of Goettingen, Goettingen, Germany

4. Torsten Hothorn

   University of Zurich

   Affiliation as printed

   Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Zurich, Switzerland