Multivariate Quantile Function Forecaster
This addresses forecasting challenges in domains like finance or energy by providing a method that captures time dependencies without error accumulation, though it is incremental as it builds on existing approaches.
The paper tackles the problem of multi-horizon probabilistic forecasting by proposing MQF$^2$, which combines autoregressive and sequence-to-sequence benefits to avoid error accumulation and model time dependencies, achieving comparable performance to state-of-the-art methods on real-world and synthetic datasets.
We propose Multivariate Quantile Function Forecaster (MQF$^2$), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are either autoregressive, implicitly capturing the dependency structure across time but exhibiting error accumulation with increasing forecast horizons, or multi-horizon sequence-to-sequence models, which do not exhibit error accumulation, but also do typically not model the dependency structure across time steps. MQF$^2$ combines the benefits of both approaches, by directly making predictions in the form of a multivariate quantile function, defined as the gradient of a convex function which we parametrize using input-convex neural networks. By design, the quantile function is monotone with respect to the input quantile levels and hence avoids quantile crossing. We provide two options to train MQF$^2$: with energy score or with maximum likelihood. Experimental results on real-world and synthetic datasets show that our model has comparable performance with state-of-the-art methods in terms of single time step metrics while capturing the time dependency structure.