论文标题
通过游览指标预测随机变量
Prediction of random variables by excursion metric projections
论文作者
论文摘要
我们将游览的概念用于预测随机变量，而无需任何时刻的假设。为此，定义了在随机变量空间上的偏移度量，这似乎是一种加权$ l^1 $ distrance。使用该指标的等效形式和游览水平的特定选择，我们将预测问题提出为最小化的某个目标功能，该目标功能涉及偏移度量。讨论了溶液的存在和预测变量的弱一致性。推出固定重尾随机功能的应用说明了上述理论的使用。通过预测高斯，$α$稳定和进一步的重尾时间序列的数值实验。
We use the concept of excursions for the prediction of random variables without any moment existence assumptions. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted $L^1$-distance. Using equivalent forms of this metric and the specific choice of excursion levels, we formulate the prediction problem as a minimization of a certain target functional which involves the excursion metric. Existence of the solution and weak consistency of the predictor are discussed. An application to the extrapolation of stationary heavy-tailed random functions illustrates the use of the aforementioned theory. Numerical experiments with the prediction of Gaussian, $α$-stable and further heavy--tailed time series round up the paper.
