New issues for the Goodness-of-fit test of the error distribution : a comparison between Sinh-arcsinh and Generalized Hyperbolic distributions

In this article, we consider a multiplicative heteroskedastic structure of financial returns and propose a methodology to study the goodness-of-fit of the error distribution. We use non-conventional estimation and model selection procedures (Berk-Jones (1978) tests, Sarno and Valente (2004) hypothesis testing, Diks et al. (2011) weighting method), based on the local volatility estimator of Mercurio and Spokoiny (2004) and the bootstrap methodology to compare the fit performances of candidate density functions. In particular, we introduce the sinh-arcsinh distributions (Jones and Pewsey, 2009) and we show that this family of density functions provides better bootstrap IMSE and better weighted Kullback-Leibler distances.