Outlier detection and estimation in nonlinear time series

The problem of identifying the time location and estimating the amplitude of outliers in nonlinear time series is addressed. A model-based method is proposed for detecting the presence of additive or innovational outliers when the series is generated by a general nonlinear model. We use this method for identifying and estimating outliers in bilinear, self-exciting threshold autoregressive and exponential autoregressive models. A simulation study is performed to test the proposed procedures and comparing them with the methods based on linear models and linear interpolators. Finally, our results are applied for detecting outliers in the Canadian lynx trappings and in the sunspot numbers data.