A0918
Title: Inference from joint distributions: Product of random variables with an application to energy market
Authors: Joanna Janczura - Wroclaw University of Science and Technology (Poland) [presenting]
Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland)
Andrzej Puc - Wroclaw University of Science and Technology (Poland)
Abstract: Multivariate analysis is a cornerstone of modern science, enabling comprehensive investigations of complex phenomena, where multiple variables interact. Despite the critical role of joint distributions of variables, in certain scientific applications, it's essential to study the product of variables rather than their joint distribution. Among many others, these are economic variables with random discount factors or tax rates, transaction values, costs of prediction errors, or variables with a random scale parameter. The aim is to study the distributional properties of a product of random variables as well as the product of vector autoregression model components. For the introduced time series, general formulas are derived for the autocovariance function, and its properties are studied for different cases of cross-dependence structure. The theoretical results are then illustrated using simulations and are applied to an electricity market case study in which the financial cost of balancing load prediction errors is analyzed after the day-ahead market settlement and prior to delivery. The considered approach yields a model that is consistent for multivariate time series as well as their product, and, on the other hand, can be an economically grounded alternative for statistical evaluation of the load (or price) forecast accuracy.
