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.
翻译:在许多应用和研究领域,时间序列的概率预测是一个重要的问题。为了从概率预测中得出结论,我们必须确保用来估计真实预测分布的模型类别足够有说服力。然而,模型本身的特征,例如不确定性或一般功能等,并不那么重要。在本文件中,我们提出了自动递增变变换模型(ATMs),这是一个由各种研究方向,例如流态正常化和自动递减模型所启发的模型类别。自动取款机利用半参数分布假设与可解释的模型规格统一了直截分布预测,并允许根据(暂时)最大相似性理论对不确定性进行量化。我们从理论上和通过对若干模拟和现实世界预测数据集进行经验评估,展示了自动取款机的特性。