Additive Outliers (AO) and Innovative Outliers (IO) in GARCH (1, 1) Processes

This study is about outlier detection in time series data. The main objective is to derive and to test statistics for detecting additive outlier (AO) and innovative outlier (IO) in GARCH(1,1) processes and subsequently to develop a procedure for testing the presence of outliers using the statistics. A test statistic has been derived for each type of outlier. In the derivation of the statistics, the method applied was to derive outlier detection statistics for GARCH(1,1) by taking the analogy of GARCH(1,1) as being equivalent to ARMA(1,1) for the 2 t ε ( t ε being the residual series). Because of the difficulty in determining the exact sampling distributions of the outlier detecting statistics, critical regions were estimated through simulations. The performance of the outlier detection was evaluated based on the outlier test criteria and the outlier detection procedure, using simulations. Results on the power of correctly detecting the outlier using the outlier test criteria and the power of correctly identifying the type of outlier, given that the location is correctly detected were reported. This was done for each type of outlier, individually. In this study the developed outlier detection procedure was applied for testing the presence of the two outlier types in the daily observations of the Kuala Lumpur Composite Index (KLCI). An outlier was found to be present in year 1998 which corresponded to the economic downturn of the 1997-1998 periods.