Enhancing the Efficiency of Time Series Forecasting by Hybrid Univariate Box Jenkins–GARCH Models

Due to the high non-linearity and volatility of the data, financial time series forecasting has been classified as a standard problem. The current study presents a method for modeling stationary, non-stationary, non-linear, and high volatility time series using a combined model of statistical methods. This study focuses on the performance of univariate Box Jenkins and the generalized autoregressive conditionally heteroscedasticity (GARCH) models in predicting financial time series and their volatility, and it presents an approach for forecasting financial time series that outperforms the performance of univariate Box Jenkins or GARCH models separately. According to the study, the performance of univariate Box Jenkins models can be improved by using the GARCH model of residuals of highly skewed data. The study's findings show that the SARIMA model is adequate for modeling the monthly Saudi General Index, with the best model being SARIMA (2, 2, 0) (2, 1, 1)4-GARCH (1, 1), with MAE, RMSE, and MAPE values of 38.2284, 57.35, and 4.247. The performance of Hybrid univariate Box Jenkins-GARCH Models shows that hybrid SARIMA-GARCH models fit financial time series and are highly accurate for short-term forecasting.