Modelling the industrial production of electric and gas utilities through the $$CIR^3$$ model

This work aims to extend previous research on how a trifactorial stochastic model, which we call \(CIR^3\), can be turned into a forecasting tool for energy time series. In particular, in this work, we intend to predict changes in the industrial production of electric and gas utilities. The model accounts for several stylized facts such as the mean reversion of both the process and its volatility to a short-run mean, non-normality, autocorrelation, cluster volatility and fat tails. In addition to that, we provide two theoretical results which are of particular importance in modelling and simulations. The first is the proof of existence and uniqueness of the solution to the SDEs system that describes the model. The second theoretical result is to convert, by the means of Lamperti transformations, the correlated system into an uncorrelated one. The forecasting performance is tested against an ARIMA-GARCH and a nonlinear regression model (NRM).