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.
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
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...
References: Aukrust, Odd (1977), “Inflation in the Open Economy: A Norwegian Model”, in Lawrence B. Krause and Walter S. Salant, eds., Worldwide Inflation, The Brookings Institution, Washington D.C., pp. 107-166. Balassa, Bela (1964), “The Purchasing Power Parity Doctrine: A Reappraisal”, Journal of Political Economy, Vol. 72, No. 6, December, pp. 584-596. Bilson, John F. O. (1979), “The Deutsche Mark/Dollar Rate – A Monetary Analysis”, in Karl Brunner and Allan H. Meltzer, eds., Policies for Employment, Prices and Exchange Rates, Carnegie-Rochester Conference 11, North-Holland, Amsterdam, pp. 59-101. Bilson, John F. O. (1978), “Rational Expectations and the Exchange Rate”, in Jacob A. Frenkel and Harry G. Johnson, eds., The Economics of Exchange Rates, Addison-Wesley Press, Reading, Massachusetts. Branson, William H. and Johan Myhrman (1976), “Inflation in Open Economies: SupplyDetermined versus Demand-Determined Models”, European Economic Review, Vol. 7, No. 1, January, pp. 15-34. Calmfors, Lars (1977), “Inflation in Sweden”, in Lawrence B. Krause and Walter S. Salant, eds., Worldwide Inflation, The Brookings Institution, Washington D.C., pp. 493544. Cárdenas, Mauricio (1997), La tasa de cambio en Colombia, Fedesarrollo, Bogotá. Cassel, Gustav (1918), “Abnormal Deviations in International Exchanges”, Economic Journal, Vol. 28, December, pp. 413-415. Cumby, Robert E. and David M. Modest (1987), “Testing for Market Timing Ability: A Framework for Forecast Evaluation”, Journal of Financial Economics, Vol. 19, No. 1, September, pp. 169-189. Cutler, David M., James M. Poterba and Lawrence H. Summers (1990), “Speculative Dynamics and the Role of Feedback Traders”, American Economic Review, Vol. 80, No. 2, May, pp. 63-68. Dooley, Michael P. and Jeff Shafer (1983), “Analysis of Short-Run Exchange Rate Behaviour: March 1973 to November 1981”, in David Bigman and Teizo Taya, eds., Exchange Rate and Trade Instability: Causes Consequences and Remedies, Ballinger, Cambridge, Massachusetts, pp. 43-49.
Dornbusch, Rudiger (1992), “Purchasing Power Parity”, in John Eatwell, Murray Milgate and Peter Newman, eds., The New Palgrave: A Dictionary of Economics, Vol. 3, Macmillan, London, pp. 236-244. Dornbusch, Rudiger (1976), “Expectations and Exchange Rate Dynamics”, Journal of Political Economy, Vol. 84, No. 6, December, pp. 1161-1176. Edgren, Gösta, Karl-Olof Faxén and Clas-Erik Odhner (1970), Lönebildning och Samhällsekonomi, Rabén och Sjögren, Stockholm, translated into English: Gösta Edgren, Karl-Olof Faxén and Clas-Erik Odner (1973), Wage Formation and the Economy, Allen & Unwin, London. Edison, Hali J. and Jan Tore Klovland (1987), “A Quantitative Reassessment of the Purchasing Power Parity Hypothesis: Evidence from Norway and the United Kingdom”, Journal of Applied Econometrics, Vol. 2, pp. 309-333. Enders, Walter (1995), Applied Econometric Time Series, Wiley, New York. Engle, Robert E. and Clive W. J. Granger (1987), “Cointegration and Error-Correction: Representation, Estimation and Testing”, Econometrica, Vol. 55, No. 2, March, pp. 251276. Engle, Robert E., Clive W. J. Granger and J. J. Hallman (1989), “Merging Short- and Long-Run Forecasts: An Application of Seasonal Cointegration to Monthly Electricity Sales Forecasting”, Journal of Econometrics, Vol. 40, No. 1, January, pp. 45-62. Flood, Robert P. and Mark P. Taylor (1996), “Exchange Rate Economics: What’s Wrong with the Conventional Macro Approach?”, in Jeffrey A. Frankel, Gaimpaolo Galli and Alberto Giovanni, eds., The Microstructure of Foreign Exchange Markets, University of Chicago Press, Chicago, pp. 261-294. Frankel, Jeffrey A. (1981), “On the Mark: Reply”, American Economic Review, Vol. 71, No. 5, December, pp. 1075-1082. Frankel, Jeffrey A. (1979), “On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials”, American Economic Review, Vol. 69, No. 4, September, pp, 610-622. Frankel, Jeffrey A. and Kenneth A. Froot (1990), “Chartists, Fundamentalists and Trading in the Foreign Exchange Markets”, American Economic Review, Vol. 80, No. 2, May, pp. 181-185. Frenkel, Jacob A. (1976), “A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence”, Scandinavian Journal of Economics, Vol. 78, pp. 200224.
Froot, Kenneth A. and Kenneth Rogoff (1995), “Perspectives on PPP and Long-Run Real Exchange Rates”, in Gene Grossman and Kenneth Rogoff, eds., Handbook of International Economics, Vol. 3, North-Holland, Amsterdam, pp. 1647-1688. Fuller, Wayne A. (1976), Introduction to Statistical Time Series, Wiley, New York. Grice-Hutchinson, Marjorie (1952), The School of Salamanca, Clarendon Press, Oxford. Hooper, Peter and John E. Morton (1982), “Fluctuations in the Dollar: A Model of Nominal and Real Exchange Rate Determinations”, Journal of International Money and Finance, Vol. 1, pp. 39-56. Isard, Peter (1995), Exchange Rate Economics, Cambridge University Press, Cambridge. Johansen, Søren (1995), Likelihood-Based Inference in Cointegrated Vector AutoRegressive Models, Oxford University Press, Oxford. Johansen, Søren (1991), “Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models”, Econometrica, Vol. 59, No. 6, November, pp. 1551-1580. Johansen, Søren (1990), The Power Function for the Likelihood Ratio Test for Cointegration, Institute of Mathematical Statistics, University of Copenhagen, Copenhagen. Johansen, Søren (1988), “Statistical analysis of cointegration vectors”, Journal of Economic Dynamics and Control, Vol. 12, No. 2-3, June-September, pp. 231-254. Johnston, John (1991), Econometric Methods, 3rd ed., McGraw-Hill, Singapore. Kim, Benjamin J. C. and Soowon Mo (1995), “Cointegration and the Long-Run Forecast of Exchange Rates”, Economic Letters, Vol. 48, No. 3-4, June, pp. 353-359. Kyle, Albert F. (1985), “Continuous Auctions and Insider Trading”, Econometrica, Vol. 53, No. 6, November, pp. 1315-1336. Lindbeck, Assar (1979), “Imported and Structural Inflation and Aggregate Demand: The Scandinavian Model Reconstructed”, in Assar Lindbeck, ed., Inflation and Employment in Open Economies, North-Holland, Amsterdam, pp. 13-40. Lyons, Richard K. (1993), “Tests of Microstructural Hypotheses in the Foreign Exchange Market”, Working Paper No. 4471, National Bureau of Economic Research, Cambridge, Massachusetts.
MacDonald, Ronald and Mark P. Taylor (1994), “The Monetary Model of the Exchange Rate: Long-Run Relationships, Short-Run Dynamics and How to Beat a Random Walk”, Journal of International Money and Finance, Vol. 13, No. 3, June, pp. 276-290. Marston, Richard C. (1987), “Real Exchange Rates and Productivity Growth in the United States and Japan”, in Sven Arndt and J. David Richardson, eds., Real-Financial Linkages Among Open Economies, MIT Press, Cambridge, Massachusetts, pp 71-96. Maynard, Geoffrey and Willy van Rijckeghem (1976), “Why Inflation Rates Differ: A Critical Examination of the Structural Hypothesis”, in Helmut Frisch, ed., Inflation in Small Countries, Lecture Notes in Economics and Mathematical Systems 119, SpringerVerlag, Berlin, pp. 47-72. Meese, Richard A. and Kenneth Rogoff (1983a), “Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?”, Journal of International Economics, Vol. 14, No. 1-2, February, pp. 3-24. Meese, Richard A. and Kenneth Rogoff (1983b), “The Out-of-Sample Failure of Empirical Exchange Rate Models: Sampling Error or Misspecification?”, in Jacob A. Frenkel, ed., (1983), Exchange Rates and International Macroeconomics, University of Chicago Press, Chicago, pp. 67-112. Officer, Lawrence H. (1982), Purchasing Power Parity and Exchange Rates: Theory, Evidence and Relevance, JAI Press, Greenwich, Connecticut. Posada P., Carlos Esteban (1999), “La tasa de interés en una economía pequeña con movilidad imperfecta de capitales: El caso colombiano del siglo XX (1905-1997)”, Borradores de Economía No. 113, Banco de la República, Bogotá. Ringstad, Vidar (1974), Prisutvikling og prisatferd i 1960-årene. En presentation og analyse av nasjonalregnskapets prisdata 1961-69, Samfunnsøkonomiske Studier 23, Statistisk Sentralbyrå (Central Brueau of Statistics of Norway), Olso. Rogoff, Kenneth (1996), ”The Purchasing Power Parity Puzzle”, Journal of Economic Literature, Vol. 34, No. 2, June, pp. 647-668. Rogoff, Kenneth (2002), “Economic Focus: Managing the World Economy”, The Economist, 3 August. Romer, David (1996), Advanced Macroeconomics, McGraw-Hill, New York. Rowland, Peter (2003), “Uncovered Interest Parity and the USD/COP Exchange Rate”, Borradores de Economía No. 227, Banco de la República, Bogotá.
Rowland, Peter and Hugo Oliveros C. (2003), “Colombian Purchasing Power Parity Analysed Using a Framework of Multivariate Cointegration”, mimeo, Banco de la República, Bogotá. Samuelson, Paul A. (1964), “Theoretical Notes on Trade Problems”, Review of Economics and Statistics, Vol. 46, May, pp. 145-154. Sweeney, Richard J. (1986), “Beating the Foreign Exchange Market”, Journal of Finance, Vol. 41. No. 1, March, pp. 163-182. Taylor, Mark P. and Helen Allen (1992), “The Use of Technical Analysis in the Foreign Exchange Market”, Journal of International Money and Finance, Vol. 11, No. 3, June, pp. 304-314. Tawadros, George B. (2001), “The Predictive Power of the Monetary Model of Exchange Rate Determination”, Applied Financial Economics, Vol. 11, No. 3, June, pp. 279-286. Villar, Leonardo and Hernán Rincón (2000), “The Colombian Economy in the Nineties: Capital Flows and Foreign Exchange Regimes”, Borradores de Economía No. 149, Banco de la República, Bogotá.
Please join StudyMode to read the full document