This study investigates the problem of outlier detection based on discrete wavelet transform in the context of time series data where the identification and treatment of outliers constitute an important component. An outlier is defined as a data point that deviates so much from the rest of observations within a data sample. In this work we focus on the application of the traditional method suggested by Tukey (1977) for detecting outliers in the closed price series of the Saudi Arabia stock market (Tadawul) between Oct. 2011 and Dec. 2019. The method is applied to the details obtained from the MODWT (Maximal-Overlap Discrete Wavelet Transform) of the original series. The result show that the suggested methodology was successful in detecting all of the outliers in the series. The findings of this study suggest that we can model and forecast the volatility of returns from the reconstructed series without outliers using GARCH models. The estimated GARCH volatility model was compared to other asymmetric GARCH models using standard forecast error metrics. It is found that the performance of the standard GARCH model were as good as that of the gjrGARCH model over the out-of-sample forecasts for returns among other GARCH specifications.

Abstract
1. Introduction
2. Wavelets and Outlier Detections
3. The MODWT Transform
    3.1. The MODWT of The Closed Price Series
    3.2. Outliers Removal Procedure
4. Model Fitting
    4.1. ARMA Model
    4.2. GARCH Model
5. Forecasting
6. Conclusion
References

• Khudhayr A. RASHEDI(PhD Student, School of Mathematical Science, Universiti Sains Malaysia, Penang, Malaysia) Corresponding Author
• Mohd T. ISMAIL(School of Mathematical Science, Universiti Sains Malaysia, Penang, Malaysia)
• S. Al WADI(Department of Risk Management and Insurance, Faculty of Business, The University of Jordan, Jordan)
• Abdeslam SERROUKH(Polydisciplinary Faculty of Larache, University Abdelmalek Essaadi, Morocco.)