Forecasting the USD/COP Exchange Rate: A Random Walk with a Variable Drift
Peter Rowland Banco de la República*

Abstract This study develops three exchange rate models as well as a simple statistical model defined as a random walk with a variable drift. The exchange rate models all use the purchasing power parity hypothesis to account for the long-term relationships between prices and the exchange rate, together with error correction models to represent any shortterm dynamics. The models are estimated for the USD/COP rate of exchange, and their forecast performance is compared to that of a simple random walk as well as to that of the random walk with a variable drift term. Two of the models are shown to outperform the simple random walk on the 12 and 24-months forecasting horizon. However, all the models are outperformed by the random walk with a variable drift, where the drift term is estimated using a Kalman filter. The results suggest that fundamental models might only be a useful tool for forecasting of the exchange rate in the very long run.

The opinions expressed here are those of the author and not necessarily of the Banco de la República, the Colombian Central Bank, nor of its Board of Directors. I express my thanks to Luis Eduardo Arango, Javier Gómez, and Luis Fernando Melo for helpful comments and suggestions. Any remaining errors are my own.

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Contents
1 2 2.1 2.2 2.3 2.4 2.5 2.6 3 3.1 3.2 3.3 3.4 3.5 3.6 4 4.1 4.2 4.3 5 Introduction Exchange Rate Models A Random Walk with a Variable Drift The Purchasing Power Parity Hypothesis The Scandinavian Model of Inflation Purchasing Power Parity and the Balassa-Samuelson Effect The Monetary Models of the Exchange Rate Brief Review of the Literature Estimation of the Models The Data Set The Different Exchange Rate Regimes in Colombia Analysing The Long-Term Cointegrating Relationships Estimating The