Predicting stock market volatility using MODWT with HyFIS and FS.HGD models

We enhance the precision of predicting daily stock market price volatility using the maximum overlapping discrete wavelet transform (MODWT) spectral model and two learning approaches: the heuristic gradient descent (FS.HGD) and hybrid neural fuzzy inference system (HyFIS). The FS.HGD approach iteratively updates the model's parameters based on the error function gradient, while the HyFIS approach combines the advantages of neural networks and fuzzy logic systems to create a more robust and accurate learning model. The MODWT uses five mathematical functions to form a discrete wavelet basis. The dataset used includes the daily closing prices of the Tadawul stock market from August 2011 to December 2019. Inputs were selected based on multiple regression, tolerance, and variance inflation factor tests, and the oil price (Loil) and repo rate (Repo) were identified as input variables. The output variable is represented by the logarithm of the Tadawul stock market price (LSCS). MODWT-LA8 (ARIMA(1,1,0) with drift) outperforms other WT functions on the 80% dataset, with an ME of (0.00000532), MAE of (0.003214182), and MAPE of (0.06449683). The addition of WT functions to the FS.HGD and HyFIS models increases their forecasting ability. Based on the reduced RMSE (0.048), MAE (0.038), and MAPE (0.538), the MODWT-LA8-FS.HGD outperforms traditional models in predicting the remaining 20% of datasets.