Modelling and Forecasting of Exchange Rate Pairs Using the Kalman Filter

Developing and employing practically useful and easy to calibrate models for prediction of exchange rates remains a challenging task, especially for highly volatile emerging market currencies. In this paper, we propose a novel approach for joint prediction of correlated exchange rates for two different currencies with respect to the same base currency. For this purpose, we reformulate a generalized version of a bivariate ARMA model into a state space model and use the Kalman filter for estimation and forecasting of the underlying exchange rates as latent variables. With extensive numerical experiments spanning 18 different exchange rates (across both emerging markets, developing and developed economies), we demonstrate that our approach consistently outperforms univariate ARMA models as well as the random walk model in short term out-of-sample prediction for various exchange rate pairs. Our study fills a gap in the empirical finance literature in terms of robust, explainable, accurate, and easy to calibrate models for forecasting correlated exchange rates. The proposed methodology has applications in exchange rate risk management as well as pricing of financial derivatives based on two exchange rates.