Abstract
We propose a new procedure for detecting a patch of outliers or influential observations for autoregressive integrated moving average (ARIMA) model using local influence analysis. It is shown that the dependency aspects of time series data gives rise to masking or smearing effects when the local influence analysis is performed using current perturbation schemes. We suggest a new perturbation scheme to take into account the dependent structure of time series data, and employ the stepwise local influence method to give a diagnostic procedure. We show that the new perturbation scheme can avoid the smearing effects, and the stepwise technique of local influence can successfully deal with masking effects. Various simulation studies are performed to show the efficiency of proposed methodology and a real example is used for illustrations.
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Acknowledgment
This research was supported by the National Natural Science Foundation of China (10761010, 11161053) and the National Natural Science Tian Yuan Foundation of China (11126297).