Statistical Investigation of Increments of Currency Rates Logarithms

Abstract

We consider the currency rates dynamics for 12 currencies, including dollar and euro, with respect to Russian rouble. We prove that the Samuelson model (geometric Brownian motion) is not suitable for this dynamics. We also prove that another model (with inverse Gaussian increments of logarithms) is not appropriate for this situation. We point out the difference in behavior of different currencies, and the difference in behavior before and during the financial crisis which began in 2008.