distribution with fractional moments arising from generalized Pearson system of differential equation.
International Journal of Advanced Statistics and Probability, 1(3), 132-141. On a probability distribution with fractional moments arising from generalized Pearson system of differential equation and its characterization. The main findings indicate that the Pearson type-IV distribution gives better results, compared with the skewed student distribution, especially at the high confidence levels, providing a very good candidate as an alternative distributional scheme.Īhsanullah, M., Shakil, M., & Kibria, B. VaR and backtesting are performed by the success–failure ratio, the Kupiec LR test, the Christoffersen independence and conditional coverage tests, the expected shortfall with ESF1 and ESF2 measures, and the dynamic quantile test of Engle and Manganelli. As case studies we consider the major historical indices of daily returns, DJIA, NASDAQ Composite, FTSE100, CAC40, DAX, and S&P500. We incorporate a GARCH model where the innovation process follows the Pearson-IV distribution, and the results are compared with the skewed Student-t distribution, in the sense of Fernandez and Steel.
This paper reconsiders the use of VaR as a measure for potential risk of economic losses in financial markets. The recent financial crisis of 2007–2009 has challenged the requirements of Basel II agreement on capital adequacy as well as, the appropriateness of value-at-risk (VaR) measurement for properly “back-tested†and “stress-tested†models.
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