The Comparison of Standard Bootstrap and Robust Outlier Detections Procedure in Bilinear (1,0,1,1) Model

Abstract

Parameter estimation is the most important part in modelling and predicting time series. However, the existence of outliers in the data will affect the estimation, which consequently jeopardizes the validity of the model. Therefore, the existence of outliers in the data must be first detected before the next process can be performed. The best outlier detection procedure can ensure data are free of outliers and achieve the best value parameter estimation. One of the procedures is using the bootstrap method to obtain the variance of the estimated magnitude of outlier effects. The variance found directly from the bootstrap method is called the 'standard' variance. However, the bootstrap method is quite complex in obtaining the variance value. As alternatives, trimming methods involving robust estimators such as a median absolute deviation (MADn) and alternative median-based deviation called Tn in the 'robust' variance calculation are used to replace the 'standard' variance. This method involves direct calculation to obtain the value of the variance from the estimated magnitude of outlier effects. To see the effectiveness of this method, the bilinear (1,0,1,1) model and two robust detection procedures, namely, modified one-step M-estimator (MOM) with MADn and MOM with Tn were used. Later, these two procedures are evaluated and compared with the bootstrap method through  simulation studies based on the probability of outlier detection. Through the findings obtained, in general, the standard bootstrap procedure performs better than the robust procedure performance in detecting the existence of outliers in the bilinear (1,0,1,1) model.