Transforming Autoregression: Interpretable and Expressive Time Series Forecast

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 general functioning are not of lesser importance. In this paper, we propose Autoregressive Transformation Models (ATMs), a model class inspired from various research directions such as normalizing flows and autoregressive models. ATMs unite expressive distributional forecasts using a semi-parametric distribution assumption with an interpretable model specification and allow for uncertainty quantification based on (asymptotic) Maximum Likelihood theory. We demonstrate the properties of ATMs both theoretically and through empirical evaluation on several simulated and real-world forecasting datasets.