Forecasting Volatility in Generalized Autoregressive Conditional Heteroscedastic (GARCH) Model with Outliers

This study aims to detect outliers and identify the best outlier detection technique and forecasting model for the financial time series data. Six outlier detection techniques and three forecasting models are compared to find the best technique and model using the daily returns data of the Pakistan Stock Exchange (PSX) 100 index from January 1996 to July 2020. The data is divided into two sections: the first estimate the model from January 1996 to December 2020, while the second produces one-day forecasts from January 2021 to July 2021. According to the research findings, the Mean Absolute Deviation (MADe) method of outlier identification outperforms the other outlier detection techniques in all three forecasting models with distinct loss functions. Furthermore, when comparing Generalized Autoregressive Conditional Heteroscedastic (GARCH) type models, Exponential Generalized Autoregressive Conditional Heteroscedastic (EGARCH (1,1)) outperforms the other two forecasting models corresponding to the reported Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). Therefore, the findings recommend that researchers use the MADe method to detect outliers and the EGARCH model as a forecasting model for financial time series data.