Probabilistic time series forecasts with autoregressive transformation models

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.

Deep transformation models for functional outcome prediction after acute ischemic stroke

“…Rügamer et al. (2021) use DTMs for time series data by including autoregressive components in the transformation function.…”

“…For instance,Sick et al (2021) andBaumann et al (2021) use 𝐹 𝑍 = Φ and predict different outcome distributions with variously flexible transformation functions on commonly used benchmark data sets in DL and demonstrate state-of-the-art prediction performances Rügamer et al (2021). use DTMs for time series data by including autoregressive components in the transformation function.1.1.5 (Deep) transformation models for ordinal outcomesThe main application of this article features an ordinal outcome (mRS).…”