Robust detection of outliers in bilinear (P,0,1,1) time series model

Bilinear time series model is the simplest model among the nonlinear time series models. Like other time series models, parameter estimation is a crucial process to determine the precision of the model. Nonlinear least squares (NLS) method along with Newton-Raphson (NR) iterative procedure is deemed as the best method to estimate parameters for bilinear Model. However, the existence of outliers will affect the accuracy of the estimated parameters. In addition, the effect of masking and swamping in outlier detection could also jeopardize the estimation. Therefore, detecting outliers and correcting its effects are vital in the construction of a good model. This study proposed two common detection procedures and two bootstrap detection procedures using robust estimators namely mommadn and momtn to improve the performance of outlier detection and to control the Type I error rate In bilinear (p,0,1,1) models, where p=1,2,3. The effectiveness of the detection procedures was evaluated based on the probability of outlier detection and the level of robustness based on Type I error rate which obtained from simulation study. This study focused on two types of outliers that are often encountered in bilinear data namely additional outlier and Innovational outlier. The findings revealed that the robust bootstrap detection procedures perform better than the other detection procedures. The parameter of bilinear (p,0,1,1) models were estimated through the robust NLS (RNLS) method. The effect of the identified outlier was removed by subtracting its estimated magnitude of outlier effect from observation and the model parameters were re-estimated on the corrected series. The Proposed four procedures and RNLS method improved the capability of outlier detection on real environmental data.