Risk prediction: a DWARF-like approach

Abstract

A large proportion of the most viable time series models used in empirical finance for density and value-at-risk forecasting are estimated with maximum likelihood methods. By way of its definition, the likelihood implicitly places equal weight on each of the observations in the sample, but this need not be optimal, depending on the extent to which the model and the true data generating process deviate. For example, in the context of modeling financial asset returns, schemes that place relatively more weight on observations in the recent past result in considerable improvement of out-of-sample density forecasts, compared with the default of equal weights. If instead of accurate forecasting of the entire density, interest is restricted to just downside risk and risk model validation, then it would seem wise to (also) place more weight on the negative observations in the sample. In this paper, such weighted likelihood schemes are proposed and demonstrated to yield considerable improvements in forecast accuracy using a variety of data sets and different GARCH models. Further improvement is realized by combining the two weighting schemes, giving rise to a doubly weighted asymmetric risk forecasting method or, in short, a DWARF-like method.