In the paper we present robust estimation methods based on bounded innovation propagation filters and quantile regression, applied to measure Value at Risk. To illustrate advantage connected with the robust methods, we compare VaR forecasts of several group of instruments in the period of high uncertainty on the financial markets with the ones modelled using traditional quasi-likelihood estimation. For comparative purpose we use three groups of tests i.e. based on Bernoulli trial models, on decision making aspect, and on the expected shortfall.

Various quantile regression approaches are implemented to analyze thecharacteristics of Italian data on earnings in the tails. A changing coefficientspattern across quantiles shows increasing returns to education along the wagedistribution. A quantile decomposition approach shows that higher educationgrants higher return at all quantiles, thus implying additional, non-linear returnsto higher education throughout the entire pattern of the earning distribution.Wage gender gap displays a decreasing pattern across quantiles, and it doesnot disappear at the higher quantiles. The southern workers penalty decreasesacross quantiles as well for highly educated workers.