A robust statistical approach to select adequate error distributions for financial returns |
| |
Authors: | J Hambuckers C Heuchenne |
| |
Institution: | 1. Chair of Statistics, Georg-August Universit?t G?ttingen, Germany;2. Fonds national de la recherche scientifique (F.R.S. – FNRS), Belgium;3. QuantOM, HEC Liege, University of Liege, Liege, Belgiumjhambuckers@ulg.ac.be;5. Institute of Statistics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium |
| |
Abstract: | In this article, we propose a robust statistical approach to select an appropriate error distribution, 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 31 D. Mercurio and V. Spokoiny, Statistical inference for time-inhomogeneous volatility models, Ann. Stat. 32 (2004), pp. 577–602.Crossref], Web of Science ®] , Google Scholar]]: the local adaptive volatility estimation. 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, and coverage probability) based on the so-obtained residuals. These methods enable to assess the global fit of a set of distributions as well as to focus on their behaviour in the tails, giving us the capacity to map the strengths and weaknesses of the candidate distributions. A bootstrap procedure is provided to compute the rejection regions in this semiparametric context. Finally, we illustrate our methodology throughout a small simulation study and an application on three time series of daily returns (UBS stock returns, BOVESPA returns and EUR/USD exchange rates). |
| |
Keywords: | Error distribution nonparametric volatility model misspecification goodness of fit selection test GARCH skewed-t NIG hyperbolic |
|
|