This empirical research aims to modeling and improving the forecasting accuracy of the volatility pattern by employing the Saudi Arabia stock market (Tadawul)by studying daily closed price index data from October 2011 to December 2019 with a number of observations being 2048. In order to achieve significant results, this study employs many mathematical functions which are non-linear spectral model Maximum overlapping Discrete Wavelet Transform (MODWT) based on the best localized function (Bl14), autoregressive integrated moving average (ARIMA) model and generalized autoregressive conditional heteroskedasticity (GARCH) models. Therefore, the major findings of this study show that all the previous events during the mentioned period of time will be explained and a new forecasting model will be suggested by combining the best MODWT function (Bl14 function) and the fitted GARCH model. Therefore, the results show that the ability of MODWT in decomposition the stock market data, highlighting the significant events which have the most highly volatile data and improving the forecasting accuracy will be showed based on some mathematical criteria such as Mean Absolute Percentage Error (MAPE), Mean Absolute Scaled Error (MASE), Root Means Squared Error (RMSE), Akaike information criterion. These results will be implemented using MATLAB software and R- software.

Abstract
1. Introduction
2. Mathematical Models
    2.1. Wavelet Transform Formula
    2.2. Autoregressive Integrated Moving-AverageModel (ARIMA)
    2.3. GARCH Model
    2.4. Volatility Computational
    2.5. Accuracy Criteria
3. Research Design and Methodology
4. Empirical Results
    4.1. Data Description
    4.2. Results and Discussion
5. Conclusion
References

• Tariq S. ALSHAMMARI(School of Mathematical Science, Universiti Sains Malaysia, Penang, Malaysia.)
• Mohd T. ISMAIL(School of Mathematical Science, Universiti Sains Malaysia, Penang, Malaysia.)
• Sadam AL-WADI(Department of Risk Management and Insurance, Faculty of Business, The University of Jordan, Jordan) Corresponding Author
• Mohammad H. SALEH(Department of Risk Management and Insurance, Faculty of Business, The University of Jordan, Jordan.)
• Jamil J. JABER(Department of Risk Management and Insurance, Faculty of Business, The University of Jordan, Jordan.)