Outliers in univariate and multivariate regression models with constraints are under consideration. The covariance matrix is assumed either to be known or to be known only partially.
The robust recursive algorithm for the parameter estimation and the volatility prediction in GARCH models is suggested. It seems to be useful for various financial time series, in particular for (high-frequency) log returns contaminated by additive outliers. The proposed procedure can be effective in the risk control and regulation when the prediction of volatility is the main concern since it is capable to distinguish and correct outlaid bursts of volatility. This conclusion is demonstrated by simulations and real data examples presented in the paper.