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, $\alpha$-stable and further heavy--tailed time series round up the paper.

翻译：我们使用外游概念来预测随机变量,而无需任何时间存在假设。为此,对随机变量空间的外游度量值作了定义,这似乎是一种加权的1美元-距离。我们使用等量的度量表和特定游览水平选择,将预测问题表述为将涉及外游度的某一目标功能最小化。讨论了解决方案的存在和预测器的不一致性。对固定的重尾随机功能的外推应用说明了上述理论的使用情况。对高山、高山、高原、高原、高山、高山、高山、高山、高山-高山-高山-高山-更长时间的预测进行数字实验。