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ABSTRACT
A diagnostic procedure for detecting additive and innovation outliers as well as level shifts in a regression model with ARIMA errors is introduced. The procedure is based on a robust estimate of the model parameters and on innovation residuals computed by means of robust filtering. A Monte Carlo study shows that, when there is a large proportion of outliers, this procedure is more powerful than the classical methods based on maximum likelihood type estimates and Kalman filtering. Copyright (C) 2001 John Wiley &Sons, Ltd.
KEY WORDS time series; additive outlier; innovation outlier; level shifts
It is well known that time series data are very often contaminated with outliers or affected by structural changes as level shifts. These disturbances can affect all the stages of time series analysis: model identification, estimation and forecasting.
The impact of outliers in the estimation of parameters of integrated autoregressive moving average (ARIMA) models has been studied, among others, by Denby and Martin (1979), Chang and Tiao (1983), Martin and Yohai (1986), Pena (1987, 1990, 1991) and Bianco et al. (1996).
Outliers may influence forecasting in two different ways:
(1) The optimal predictor for an ARIMA model depends on its parameters. Therefore, the bias in parameter estimates produced by outliers will decrease its efficiency.
(2) The optimal predictor is a linear combination of the observed data, and generally, the largest coefficients are those corresponding to observations near to the forecast origin. Therefore the presence of outliers among these observations may have a large impact on forecasts. However, the prediction error will depend on the type of outliers: an additive outlier may increase the predictor error considerably, but an innovation outlier will not have any effect. The influence of different types of outliers in forecasting can be found in Chen and Liu (1993a) and Ledolter (1988, 1991).
Several approaches have been considered for detecting outliers and structural changes in ARIMA models. One of these approaches is to use likelihood ratio tests and the resulting procedures are based on the residuals corresponding to an efficient estimate under Gaussian innovations. Likelihoodbased methods of this type were proposed for autoregressive models by Fox (1972) and extended for ARMA models by Chang, Tiao, and Chen (1988), Tsay (1988) and Chen and Liu (1993b). Otto...