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

Conference (2013, April 19)

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 ... [more ▼]

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. [less ▲]

Modélisation d'évènements rares à l'aide de distributions non normales : application en finance avec la fonction sinh-arcsinh

Master's dissertation (2011)

In 2008, the financial crisis put forward the relative inaccuracy of the market risk forecasting models in the financial industry. In particular, extreme events were shown to be regularly underestimated ... [more ▼]

In 2008, the financial crisis put forward the relative inaccuracy of the market risk forecasting models in the financial industry. In particular, extreme events were shown to be regularly underestimated. This problematic, initially developed in the seminal work of Mandelbrot (1963), is mainly due to financial models using the normal law while empirical evidence show strong leptokurticity in financial time series. This stylized effect is particularly damaging the forecasting of indicators like Value-at-Risk (VAR). In this study, we try to tackle problem by testing a newly-developed probability distribution, never used in finance: sinh-arcsinh function. By creating different datasets from non-parametric and GARCH models, we adjust common functions (normal, t location-scale, GED, gen. hyperbolic) and sinh-arcsinh function on the data. We show that, regarding the leptokurtic datasets extracted from the DJA and the NIKKEI 225, the sinh-arcsinh function performs a better adjustment than any other function tested. We also tested simple VAR models using normal laws, Student’s t or sinh-arcsinh functions, to assess the operational efficiency of the sinh-arcsinh function. We show that models using sinh-arcsinh functions provide more accurate and better in-sample and out-of-sample VAR forecasts than any other model using the normal laws. [less ▲]