Forecasting Stock Volatility Using Wavelet-based Exponential Generalized Autoregressive Conditional Heteroscedasticity Methods

Abstract

In this study, we proposed a new model to improve the accuracy of forecasting the stock market volatility pattern. The hypothesized model was validated empirically using a data set collected from the Saudi Arabia stock Exchange (Tadawul). The data is the daily closed price index data from August 2011 to December 2019 with 2027 observations. The proposed forecasting model combines the best maximum overlapping discrete wavelet transform (MODWT) function (Bl14) and exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model. The results show the model's ability to analyze stock market data, highlight important events that contain the most volatile data, and improve forecast accuracy. The results were compared from a number of mathematical models, which are the non-linear spectral model, autoregressive integrated moving average (ARIMA) model and EGARCH model. The performance of the forecasting model will be evaluated based on some of error functions such as Mean absolute percentage error (MAPE), Mean absolute scaled error (MASE) and Root means squared error (RMSE).

Predicting Stock Market Volatility Using MODWT with HyFIS and FS.HGD Models

“…On the other hand, the MODWT-LA8-HyFIS model has the highest RMSE and MAE values of 0.604 and 0.423, respectively, and the highest MAPE value of 6.794, indicating the lowest level of accuracy among all models. Several aspects distinguish the current study from the previous study conducted by (Alshammari et al 2023). Firstly, we propose two new hybrid models, namely HyFIS and FS.HGD, in conjunction with five functions of MODWT, whereas the previous study employed only the gradient descent learning (FIR.DM) model combined with MODWT.…”

“…In terms of accuracy and out-of-sample prediction performance, the RF model demonstrates superior performance compared to other commonly used methods for predicting stock market returns, including linear regression and neural networks. Alshammari et al (2023) introduced a novel approach to predicting stock market volatility using a wavelet-based exponential GARCH (EGARCH) model. The authors proposed a hybrid model that combines the EGARCH model with the most effective MODWT function to improve the accuracy of stock market volatility forecasting.…”

“…The primary distinction between DWT and MODWT is the former can only be used with a limited number of observations, while the latter may be used with any quantity of data. WT is an extension of the Fourier transform (Alshammari et al 2023;Adil 2015). It is divided into two types: the mother wavelet φ(t), which defines the high-frequency components or detailed coefficients, and the father wavelet ϕ(t), which represents the low-frequency components or smooth coefficients as indicated in (2) and (3), respectively (Al-Wadi et al 2022).…”

“…The father wavelets and mother wavelets need to meet the requirements of φ(t)dt = 1 and ϕ(t) dt = 0. The MODWT provides several useful transform functions, including Haar, Daubechies (d4), Coiflet (C6), least asymmetric (LA8), and best-localized (bl14) (Jaber et al 2017;Alshammari et al 2023).…”

“…One area of focus is the study of volatility in stock market data, which refers to the degree of variation in a stock's price over time. Volatility analysis is critical for investors and financial analysts in predicting potential risks and returns on investments (Alshammari et al 2023).…”