On the Generalized Pearson Distribution for Application in Financial Time Series Modeling

Abstract

We elaborate on a new distributional scheme resulting from the generalised Pearson distribution with application to financial modelling. As case studies, we consider the major historical indices daily returns, DJIA, NASDAQ composite, FTSE100, CAC40, DAX and S%P500, as well as, high-frequency returns of the Euro/Japanese Yen foreign currency exchange rates. Using non-linear optimisation techniques, we compare the results of the maximum likelihood estimator of the new distribution to the results of the Pearson type-IV distribution. The main findings indicate that the new distribution improves the value of the estimator in all cases, with significant improvement below the 60-min sampling.