Exchange Rate Forecast Model

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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 Error Correction Models The Johansen Framework Likelihood Estimation and Results Forecasting the USD/COP Exchange Rate The Methodology for Evaluating the Forecasts Comparing the Models A Comment on Long-Term Forecasting of the Exchange Rate Conclusion

References

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1 Introduction
Modelling and forecasting exchange rates using fundamentals is a hazardous activity. In 1983, Richard A. Meese and Kenneth Rogoff wrote their seminal paper, Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?,1 where they showed that the main empirical exchange rate models have inferior out-of-sample forecasting ability compared to naïve models such as a random walk. These rather gloomy results have turned out to be very difficult to overturn, and they have been confirmed by a large number of studies. Some recent studies, using not only the long-term relationships between fundamental variables and the exchange rate but also the short-term dynamics between the variables represented by an error correction model, have, nevertheless, shown some positive results.2 This study develops three such models for the USD/COP exchange rate,3 and compares their forecasting performance to that of a simple random walk as well as with that of a random walk process with a variable drift term. The first two exchange rate models use an Engle, Granger and Hallman (1989) framework, where a long-term cointegrating relationship based on purchasing power parity (PPP) is estimated using quarterly data from 1973 up until 2002. This is combined with an error correction model estimated with data from 1992 up until 2002. For the first model the error correction model is based on a PPP framework, and for the second on the framework of a monetary model. Both these models are shown to outperform a simple random walk on the 12 and 24-month forecasting horizon. The model using monetary data also outperforms the simple random walk on the 6-month horizon.

Meese and Rogoff (1983a). See, for example, Kim and Mo (1995), MacDonald and Taylor (1984), Rowland and Oliveros (2003), and Tawadaros...
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