Time series forecasting is difficult. It is difficult even for recurrent
neural networks with their inherent ability to learn sequentiality. This
article presents a recurrent neural network based time series forecasting
framework covering feature engineering, feature importances, point and interval
predictions, and forecast evaluation. The description of the method is followed
by an empirical study using both LSTM and GRU networks.

本文介绍了一种基于递归神经网络的时间序列预测框架，包括特征工程、特征重要性、点和区间预测以及预测评估，并使用 LSTM 和 GRU 网络进行了实证研究。

时间序列预测的循环神经网络

Recurrent Neural Networks for Time Series Forecasting

Strictly proper kernel scores are well-known tool in probabilistic
forecasting, while characteristic kernels have been extensively investigated in
the machine learning literature. We first show that both notions coincide, so
that insights from one part of the literature can be used in the other. We then
show that the metric induced by a characteristic kernel cannot reliably
distinguish between distributions that are far apart in the total variation
norm as soon as the underlying space of measures is infinite dimensional. In
addition, we provide a characterization of characteristic kernels in terms of
eigenvalues and -functions and apply this characterization to the case of
continuous kernels on (locally) compact spaces. In the compact case we further
show that characteristic kernels exist if and only if the space is metrizable.
As special cases of our general theory we investigate translation-invariant
kernels on compact Abelian groups and isotropic kernels on spheres. The latter
are of particular interest for forecast evaluation of probabilistic predictions
on spherical domains as frequently encountered in meteorology and climatology.

本文以概率预测为背景，探究了特征核、协方差核及它们联系的性质及应用，着重探讨了特征核在测度空间无限维中的效果、特征核存在条件以及在一些天气学领域的预测中的应用。