Out of sample Value-at-Risk and backtesting with the standardized Pearson type-IV skewed distribution

Abstract

This paper studies the efficiency of an econometric model where the volatility is modeled by a GARCH (1,1) process, and the innovations follow a standardized form of the Pearson type-IV distribution. The performance of the model is examined by in sample and out of sample testing, and the accuracy is explored by a variety of Value-at-Risk methods, the success/failure ratio, the Kupiec-LR test, the independence and conditional coverage tests of Christoffersen, the expected shortfall measures, and the dynamic quantile test of Engle and Manganelli. Overall, the proposed model is a valid and accurate model performing better than the skewed Student-t distribution, providing the financial analyst with a good candidate as an alternative distributional scheme.