Recursive estimation in autoregressive models with additive outliers

This work deals with recursive robust estimation in autoregressive models that are contaminated by additive outliers. The importance of such procedures in applied time series is obvious: (i) the recursive character of the estimation allows to treat time series in real time (on-line) updating previous estimates by means of simple calculations after delivering new observations; (ii) robustness of the estimation procedures makes them insensitive to outlied observations that can distort significantly results of classical non-robust estimation procedures (the additive outliers have also unpleasant consequences for forecasting, see e.g. [10], [14]). The autoregressive model of the order p with additive outliers denoted as AOAR(p) has the form yt = Xt + Vt, (1A) where xt (pixt-i + ••• + (fpxt-p +£t (1.2)