The statistical distribution of exchange rates: Empirical evidence and economic implications

Abstract

The abundant evidence that changes in exchange rates have distributions with fatter tails than the normal distribution has led researchers to consider non-normal distributions, including the Student, the stable Paretian and mixtures of distributions. This paper compares the empirical fits of three non-normal candidates and the normal distribution for daily changes in the logarithms of exchange rates, using maximum likelihood estimation of the parameters and chi-square goodness-of-fit tests. The Student and mixture of two normals provide the best fits, but there is evidence that the distribution parameters may vary over time.