A new methodological approach for error distributions selection
Julien Hambuckers, Cédric Heuchenne · Open Repository and Bibliography (University of Liège) · 2013
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).