Wavelet Based Detection of Outliers in Volatility Time Series Models

We introduce a new wavelet based procedure for detecting outliers in financial discrete time series.The procedure focuses on the analysis of residuals obtained from a model fit,and applied to the Generalized Autoregressive Conditional Heteroskedasticity(GARCH)like model,but not limited to these models.We apply the Maximal-Overlap Discrete Wavelet Transform(MODWT)to the residuals and compare their wavelet coefficients against quantile thresholds to detect outliers.Our methodology has several advantages over existing methods that make use of the standard Discrete Wavelet Transform(DWT).The series sample size does not need to be a power of 2 and the transform can explore any wavelet filter and be run up to the desired level.Simulated wavelet quantiles from a Normal and Student t-distribution are used as threshold for the maximum of the absolute value of wavelet coefficients.The performance of the procedure is illustrated and applied to two real series:the closed price of the Saudi Stock market and the S&P 500 index respectively.The efficiency of the proposed method is demonstrated and can be considered as a distinct important addition to the existing methods.

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

In this study,we proposed a new model to improve the accuracy of fore-casting the stock market volatility pattern.The hypothesized model was validated empirically using a data set collected from the Saudi Arabia stock Exchange(Tada-wul).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 mod-els,which are the non-linear spectral model,autoregressive integrated moving aver-age(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).