A new methodological approach for error distributions selection

Since 2008 and its financial crisis, an increasing attention has been devoted to the selection of an adequate error distribution in risk models, in
particular for Value-at-Risk (VaR) predictions. We propose a robust methodology to select the most appropriate error distribution candidate, in a
classical multiplicative heteroscedastic model. In a first step, unlike to the traditional approach, we do not use any GARCH-type estimation of the
conditional variance. Instead, we propose to use a recently developed nonparametric procedure: the Local Adaptive Volatility Estimation (LAVE).
The motivation for using this method is to avoid a possible model misspecification for the conditional variance. In a second step, we suggest
a set of estimation and model selection procedures tests based on the so-obtained residuals. These methods enable to assess the global fit of a
given distribution as well as to focus on its behaviour in the tails. Finally, we illustrate our methodology on three time series (UBS stock returns,
BOVESPA returns and EUR/USD exchange rates).