B0936
Title: Prediction of random variables by excursion metric projections
Authors: Vitalii Makogin - Ulm University (Germany) [presenting]
Evgeny Spodarev - Ulm University (Germany)
Abstract: The concept of excursions is used 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 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. The existence of the solution and the 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 demonstrate a good performance of our method.
