Forecasting real effective exchange rate indices of currencies using a stochastic factor

Abstract

This article considers the possibility of forecasting real effective exchange rate indices for leading world countries. A stable unified mean trajectory for a reliable forecast of the index cannot be constructed using data from 31 January 1994 to 30 April 2017; however, it is reasonable to use data of the last period for this purpose. To construct a short-term forecast of real effective exchange rates based on initial value, we propose using a simulation with a discrete approximation of stochastic differential equations of Merton, Vasicek, Dosen, Ogden, and Cox-Ingersoll-Ross, and a polynomial residues model. Simulations using discrete approximations of the Vasicek, Merton, Dosen, and Ogden equations did not allow constructing a reliable forecast of the specified index using data from April 2016 to March 2017 for the USA, UK, Eurozone countries, Japan, and Switzerland. Processing simulation results based on a discrete approximation of the stochastic Cox-Ingersoll-Ross equation and the polynomial residues model, and for the considered countries for most of the same time period, resulted in a 50 % confidence interval for the mean trajectory of observed values of effective exchange rates indexes. The quality of the forecast essentially depends on the selected time period and methods used to determine the numerical parameters of discrete approximations for the original stochastic equations.