Highly flexible distributions to fit multiple frequency financial returns

Abstract

Financial data are usually studied via low flexible distributions, independently of the frequency of the data, due to their simplicity and analytical tractability. In this paper we analyze two highly flexible five-parameter distributions into fitting financial returns, these are the skewed generalized t (SGT) and the generalized hyperbolic (GH). Applications carried on two exchange rates (Euro–Dollar and Dollar–Yen), and two indexes (S&P 500 and Nikkei 225) over four frequencies: weekly, daily, 30-min and 5-min, confirm the superiority of the SGT and GH in approximating the distribution of a given data at a remarkable precision. Moreover, as we move from higher to lower frequency, the distribution’s overall shape does indeed change radically, and the estimated parameters refute the tendency to normality, which calls into question the aggregational Gaussianity’s stylized fact.