Abstract
This chapter discusses robustness of univariate time series forecasting based on ARIMA time series models. Under complete prior knowledge, optimal forecasting statistics are constructed for the following undistorted hypothetical models: stationary time series models, AR(p), MA(q), ARMA(p, q), and ARIMA(p, d, q) models. Plug-in forecasting statistics are constructed for different types of prior uncertainty. Robustness of the obtained forecasting algorithms is evaluated under the following distortion types: parametric model specification errors, functional distortions of the innovation process in the mean value, heteroscedasticity, AO and IO outliers, bilinear autoregression distortions.
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