Hybrid fuzzy inference rules of descent method and wavelet function for volatility forecasting

This research employs the gradient descent learning (FIR.DM) approach as a learning process in a nonlinear spectral model of maximum overlapping discrete wavelet transform (MODWT) to improve volatility prediction of daily stock market prices using Saudi Arabia's stock exchange (Tadawul) data. The MODWT comprises five mathematical functions and fuzzy inference rules. The inputs are the oil price (Loil) and repo rate (Repo) according to multiple regression correlation, and the Engle and Granger Causality test Engle RF, (1987). The logarithm of the stock market price (LSCS) in Tadawul reflects the output variable. The correlation matrix reveals that there is no collinearity between the input variables, and the causality test demonstrates that the input variables significantly influence the outcome variable. According to the multiple regression, there is a substantial negative influence between Loil and LSCS but a significant positive effect between Repo and output. For the 80% dataset under ME (0.000005), MAE (0.003214), and MAPE (0.064497), the MODWT-LA8 (ARIMA(1,1,0) with drift) for the LSCS variable performs better than other WT functions. In the novel hybrid model MODWT-FIR.DM, each function's approximation coefficient (LSCS) is applied with input variables (Loil and Repo). We evaluate the performance of the proposed model (MODWT-LA8-FIR.DM) using different statistical measures (ME, RMSE, MAE, MPE) and compare it to two established models: the original FIR.DM and other MODWT-FIR.DM functions for forecasting 20% of datasets. The outcomes show that the MODWT-LA8-FIR.DM performs better than the traditional models based on lower ME (3.167586), RMSE (3.167638), MAE (3.167586), and MPE (80.860849). The proposed hybrid model may be a potential stock market forecasting model.