Volatility GARCH models with the ordered weighted average (OWA) operators

Abstract

Volatility is an important issue for companies, policy-makers, and researches. Autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH (GARCH) models are frequently used to study volatility. However, forecasting efficiency tends to fail when complex data is used. This paper proposes the use of ordered weighted average (OWA) operators in combination with ordinary least squares (OLS) to create an estimator that can treat high degrees of uncertainty. In the application of the ARCH-GARCH models, we develop approaches with the OWA and the induced OWA operator. Some further generalizations are also developed by using generalized means. The main advantage of this new methodology is to add additional information to the process of estimating the models according to the attitudinal character of the decision-maker. Finally, the work presents an application in the volatility of the MX/US exchange rate, where the efficiency of the OWA operators in forecasting is proved.