Forecasting the UK Pound/US Dollar Exchange Rate with a Continuous Time Macroeconometric Model

Over the last 40 years, researchers have unsuccessfully tried to overturn the puzzling result of Meese and Rogoff (1983), according to which a simple random walk without drift is a better ex post predictor of the nominal exchange rate. This paper argues that the key to the resolution of the puzzle lies in moving away from linear, single equation models in order to adopt systems of nonlinear simultaneous equations describing the behaviour of the whole economy. In order to test this hypothesis, a small sized continuous time macroeconometric model of the United Kingdom is developed with the primary purpose forecasting the Pound/Dollar spot exchange rate. The model consist of 20 simultaneous differential equations, with 8 exogenous variables and 77 parameters. The data sample used for estimation is quarterly, running from 1975Q1 to 2019Q4. The system will be estimated by applying Full Information Maximum Likelihood estimator to a stochastically equivalent exact discrete-time analogue of the continuous system. The forecasting performance of the model will be gauged against the standard random walk without drift. Several forecast evaluation tests are proposed and discussed.., researchers have unsuccessfully tried to overturn the puzzling result of Meese and Rogoff (1983)., according to which a simple random walk without drift is a better ex post predictor of the nominal exchange rate. This paper argues that the key to the resolution of the puzzle lies in moving away from linear., single equation models in order to adopt systems of nonlinear simultaneous equations describing the behaviour of the whole economy. In order to test this hypothesis., a small sized continuous time macroeconometric model of the United Kingdom is developed with the primary purpose forecasting the Pound/Dollar spot exchange rate. The model consist of 20 simultaneous differential equations., with 8 exogenous variables and 77 parameters. The data sample used for estimation is quarterly., running from 1975Q1 to 2019Q4. The system will be estimated by applying Full Information Maximum Likelihood estimator to a stochastically equivalent exact discrete-time analogue of the continuous system. The forecasting performance of the model will be gauged against the standard random walk without drift. Several forecast evaluation tests are proposed and discussed.