Probabilistic Forecasting with Spline Quantile Function RNNs

Jan A. Gasthaus · Konstantinos Benidis · Syama Sundar Rangapuram · David Salinas · Valentín Flunkert · Tim Januschowski

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Forecasting Techniques and Applications Neural Networks and Applications Time Series Analysis and Forecasting

Abstract

In this paper, we propose a flexible method for probabilistic modeling with conditional quantile functions using monotonic regression splines. The shape of the spline is parameterized by a neural network whose parameters are learned by minimizing the continuous ranked probability score. Within this framework, we propose a method for probabilistic time series forecasting, which combines the modeling capacity of recurrent neural networks with the flexibility of a spline-based representation of the output distribution. Unlike methods based on parametric probability density functions and maximum likelihood estimation, the proposed method can flexibly adapt to different output distributions without manual intervention. We empirically demonstrate the effectiveness of the approach on synthetic and real-world data sets.

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References

1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1977Time Series Analysis: Forecasting and Control 2007Strictly Proper Scoring Rules, Prediction, and Estimation 2000Designing and managing the supply chain : concepts, strategies, and case studies 2017A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction 1976Scoring Rules for Continuous Probability Distributions 2010Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules 2000A quantile regression neural network approach to estimating the conditional density of multiperiod returns

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