Modelling commodity value at risk with higher order neural networks

The motivation for this article is to investigate the use of a promising class of Neural Network (NN) models, Higher Order Neural Networks (HONNs), when applied to the task of forecasting the 1-day ahead Value at Risk (VaR) of the brent oil and gold bullion series with only autoregressive terms as inputs. This is done by benchmarking their results with those of a different NN design, the Multilayer Perceptron (MLP), an Extreme Value Theory (EVT) model along with some traditional techniques, such as an Autoregressive Moving Average Model-Generalized Autoregressive Conditional Heteroscedasticity (ARMA-GARCH) (1,1) model and the RiskMetrics volatility. In addition to these, we also examine two hybrid NNs-RiskMetrics volatility models. More specifically, the forecasting performance of all models for computing the VaR of the brent oil and the gold bullion is examined over the period 2002 to 2008 using the last year for out-of-sample testing. The evaluation of our models is done by using a series of backtesting algorithms and two loss functions: a violation ratio calculating when the realized return exceeds the forecast VaR and an average squared violation magnitude function, firstly introduced in this article, computing the average magnitude of the violations. As it turns out, the hybrid HONNs-RiskMetrics model does remarkably well and outperforms all other models in forecasting the VaR of gold and oil at both the 5% and 1% confidence levels, providing an accurate number of independent violations which also have the lowest magnitude on average. The pure HONNs and MLPs along with the hybrid MLP-RiskMetrics model also give satisfactory forecasts in most cases.