A new generalization of skew-T distribution with volatility models


Altun E. , Tatlidil H., Ozel G. , Nadarajah S.

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, vol.88, no.7, pp.1252-1272, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 88 Issue: 7
  • Publication Date: 2018
  • Doi Number: 10.1080/00949655.2018.1427240
  • Title of Journal : JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
  • Page Numbers: pp.1252-1272

Abstract

In this paper, we propose a new generalized alpha-skew-T (GAST) distribution for generalized autoregressive conditional heteroskedasticity (GARCH) models in modelling daily Value-at-Risk (VaR). Some mathematical properties of the proposed distribution are derived including density function, moments and stochastic representation. The maximum likelihood estimation method is discussed to estimate parameters via a simulation study. Then, the real data application on S&P-500 index is performed to investigate the performance of GARCH models specified under GAST innovation distribution with respect to normal, Student's-t and Skew-T models in terms of the VaR accuracy. Backtesting methodology is used to compare the out-of-sample performance of the VaR models. The results show that GARCH models with GAST innovation distribution outperforms among others and generates the most conservative VaR forecasts for all confidence levels and for both long and short positions.