On the performance of GARCH family models using the root mean square error and the mean absolute error

It is a common practice to detect outliers in a financial time series in order to avoid the adverse effect of additive outliers. This paper investigated the performance of GARCH family models (sGARCH; gjrGARCH; iGARCH; TGARCH and NGARCH) in the presence of outliers (small, medium and large) for different time series lengths (250, 500, 750, 1000, 1250 and 1500) using the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE). In a simulation iteration of 1000 times in R environment using rugarch, results revealed that for small size of outliers, irrespective of the length of time series, iGARCH was superior, for medium size of outliers, it was sGARCH and gjrGARCH that were superior irrespective of the time series length, and for a large size of outliers, irrespective of the time series length, gjrGARCH was superior. The study leveled that in the presence of additive outliers, both RMSE and MAE values would increase as the time series length is increased.