Robust bootstrap procedures for detecting additional and innovational outliers in bilinear (1, 0, 1, 1) model

Abstract

Time series models can be classified into linear and nonlinear where among the nonlinear models, the simplest is bilinear model. The process of estimating model parameters is an important phase for time series modeling. However, the existence of outliers in the data will affect the estimated parameters, which consequently will jeopardize the validity of the model. To alleviate this problem, the existence of outliers in the data must first be detected before further actions could be taken. Therefore, it is crucial to step up the outlier detection procedure to get the best parameter estimation results. Obtaining the magnitude of outlier effects is generally done using a bootstrap method yielding classical bootstrap mean and variance. However, with existence of outliers, the classical bootstrap variance value may be slightly disturbed. Therefore, this study proposed two robust detection procedures namely bootstrap-MOM with MADn and bootstrap- MOM with Tn to improve the performance of outlier detection for additional outlier and innovational outlier in bilinear (1,0,1,1) model. Modified one-step M-step (MOM) is a known robust location estimator while Median Absolute Deviation (MADn) and alternative median based deviation called Tn are known as robust scale estimators. For the magnitude of outlier effect, MOM is used to obtain the mean while MADn and Tn are used separately to estimate variance. The performance of bootstrap-MOM with MADn and Tn procedures for outlier detection is found better compared to the classical procedure. The suggested robust outlier detection procedures proposed in this study are beneficial to improve the parameter estimation of bilinear models.