Dependence structure for the product of bi-dimensional finite-variance VAR(1) model components. An application to the cost of electricity load prediction errors

TL;DR

This paper analyzes the dependence structure of the product of bi-dimensional VAR(1) model components, deriving autocovariance formulas, studying cross-dependence effects, and applying findings to electricity load prediction errors.

Contribution

It introduces formulas for autocovariance of the product of VAR(1) components and explores their properties under different cross-dependence scenarios, with practical application to electricity market data.

Findings

Derived autocovariance formulas for the product of VAR(1) components.

Demonstrated effects of cross-dependence on autocovariance structure.

Applied theoretical results to real electricity load data.

Abstract

In this paper we analyze the product of bi-dimensional VAR(1) model components. For the introduced time series we derive general formulas for the autocovariance function and study its properties for different cases of cross-dependence between the VAR(1) model components. The theoretical results are then illustrated in the simulation study for two types of bivariate distributions of the residual series, namely the Gaussian and Student's t. We also show a possible practical application of the obtained results based on the data from the electricity market.