A new methodological approach for error distributions selection in Finance

In this article, 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 don't use any GARCH-type estimation of the conditional variance. Instead, we propose to use a recently developed nonparametric procedure (Mercurio and Spokoiny, 2004): 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 (Berk-Jones tests, kernel density-based selection, censored likelihood score, coverage probability) 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 behavior in the tails. Finally, we illustrate our methodology on three time series (UBS stock returns, BOVESPA returns and EUR/USD exchange rates).