Abstract

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are often used in finance to predict how volatility changes over time. They help capture things like varying volatility, patterns in data, and other characteristics in financial data. Usually, researchers use log-returns to study these patterns. Past studies tried using different probability distributions to estimate the GARCH process, but they did not do a good job accounting for changing volatility and other patterns in financial data, leading to inaccurate predictions. This study suggests using a robust neural network architecture, known as the Jordan Neural Network (JNN) to improve the GARCH process. Hence, this study is aimed at creating JNN-GARCH models with better predictions and model parameters, especially when dealing with asymmetric patterns in the data.
Considered for this study were two error innovations: the Generalised Length Biased Scaled-t (GLBST) and Generalised Beta Skewed-t (GBST) distributions, derived by modifying the Fisher Concept of Weighted Distribution and the McDonald Generalised Beta Function, respectively, in the Student-t distribution. The proposed innovations were applied to JNN (1,1,1)-GARCH (1,1) models, to derive the JNN(1,1,1)-GARCH(1,1)-GLBST and JNN (1,1,1)-GARCH(1,1)-GBST models. A daily oil price dataset spanning from January 12, 2012, to December 29, 2022, obtained from the West Texas Intermediate (WTI) market was used to illustrate the models. Performance was compared with standard Neural Networks, classical GARCH, and Asymmetric Power ARCH (APARCH) models, considering different error innovation distributions such as Normal, Student-t, GED, GBST, and GLBST. Model validation criteria included log-likelihood, Mean Square Error (MSE), and Akaike Information Criterion (AIC).

Results indicated that crude oil prices exhibit non-stationary behavior, while log returns display stationarity with clustered volatility. Various tests and plots, such as the Shapiro test, Augmented Dickey Fuller test, skewness and kurtosis, Autocorrelation, and Partial Autocorrelation Plots, point towards a time series data pattern with non-constant variance. A total of twenty-three models were under consideration. Among them, the JNN(1,1,1)-GARCH-GLBST(1,1) model with 17 Units and 107 Connections demonstrated superior performance, outperforming other models. Additionally, the JNN(1,1,1)-GARCH-GLBST(1,1) model with 11 Units and 104 Connections, along with GARCH-GBST(1,1), GARCH(1,1) -Student-t, APARCH(1,1)- Skewed Normal models, were part of the analysis. Comparison based on AIC values (10.493, 11.765, 44.355, 81.706, and 83.706) favored the JNN(1,1,1)-GARCH-GLBST(1,1) model with 17 Units and 107 Connections.
The Jordan Neural Network in GARCH variations with asymmetric innovations has proven to have superior error performance compared to other GARCH versions, Neural Networks, and a simplified Jordan Neural Network. These suggested models present a viable alternative for modeling the volatility of both symmetric and asymmetric crude oil returns data.