Department of Business Administration Master’s Thesis---- Spring 2006 Supervisor: Jörgen Hellström Authors: Ying Zhang Hailun Wu A comparison of the prediction performances by the linear models and the ARIMA model Take AUD/JPY as an example ACKNOWLEDEGMENTS We would like to thank our supervisor Mr. Jörgen Hellström who provided us with continuous and instructive feedback during the progress of the work. He was always very patient, careful and helpful, and he spent a lot of time on our thesis. Thank you for your support. Furthermore, we would like to thank the Umeå school of Business Administration which provides us with good facilitates and knowledgeable teachers. Finally, we would like to thank those who have helped and encouraged us, especially our parents. Without their help we will not finish our study. Ying Zhang and Hailun Wu Abstract With the development of the financial markets, the foreign exchange market has become more and more important for investors. The daily volume of business dealt with on the foreign exchange markets in 1998 was estimated to be over $2.5 trillion dollars (the daily volume on New York Stock Exchanges is about $20 billion). Today (2006) it may be about $5 trillion dollars. More and more people notice the foreign exchange market, and more and more sophisticated investors research such markets. The purpose of this thesis is to compare different methods to forecast the exchange rate of the money pair AUD/JPY. Firstly we studied the relationship between the AUD/JPY exchange rate and some economic fundamentals by using a regression model. Secondly, we tested whether the AUD/JPY exchange rate had any relationship with its historical records by using an ARIMA model. Finally, we compared the two model forecasting performance. A secondary purpose is to test whether the Market Efficiency Hypothesis works on the money pair AUD/JPY. In the study, data from January 1986 to June 2006 were chosen. To test which method produces better forecasts, we chose data from January 1986 to December 2002 to build up the prediction functions. Then we used the data from January 2003 to 2006 June to evaluate which predicting method was closer to the reality. In the comparison of the forecasting performances, two approaches dealing with the unknown future fundamentals were used. Firstly we assumed that we could do perfect predictions of these regressors, that was, our predictions of these regressors were the same as the actual future outcomes. So we put the real data for the fundamentals from January 2003 to June 2006 into the regression function. Secondly we assumed that we were in real life situation, and we had to predict the regressors first in order to get the predictions of the exchange rate. The results of the comparison were that the AUD/JPY exchange rate could to some extent be predictable, and that the predictions by the ARIMA model were more accurate. Key words: Foreign exchange market, AUD/JPY, regression model, ARIMA model Table of contents Chapter one: Introduction .................................................................................................................3 1.1 Background .........................................................................................................................3 1.2 Purpose of this paper...........................................................................................................4 1.3 The limitation of the study ..................................................................................................4 1.4 Definitions...........................................................................................................................5 1.5 The outline of the paper ......................................................................................................6 Chapter Two: Methodology ..............................................................................................................7 2.1 Choice of subject and preconceptions.................................................................................7 2.2 Scientific approach..............................................................................................................7 2.3 Research method.................................................................................................................8 2.4 The collection of data..........................................................................................................9 Chapter Three: The foreign exchange market and general information of the AUD/JPY exchange rate ..................................................................................................................................................10 3.1 Introduction of foreign exchange market..........................................................................10 3.2 The determination of exchange rates ................................................................................11 3.3 Basic knowledge of quoting..............................................................................................13 3.4 Literature review...............................................................................................................13 3.5 General information of the money pair AUD/JPY............................................................14 3.5.1 The Australian dollar..............................................................................................14 3.5.2 The Japanese yen....................................................................................................15 3.5.3 Characteristics of the money pair AUD/JPY..........................................................16 Chapter Four: Theories ...................................................................................................................17 4.1 Purchasing Power Parity (PPP).........................................................................................17 4.2 The International Fisher Effect (IFE)................................................................................18 4.3 Economic Growth .............................................................................................................19 4.4 Efficiency market hypothesis............................................................................................19 4.5 The selection of the economic fundamentals ....................................................................20 Chapter Five: Empirical study ........................................................................................................23 5.1 Fundamental model...........................................................................................................23 5.2 ARIMA model...................................................................................................................26 5.3 Forecasting performance...................................................................................................35 Chapter six: Conclusion..................................................................................................................39 Chapter seven: Credibility criteria ..................................................................................................41 7.1 Validity..............................................................................................................................41 7.2 Reliability..........................................................................................................................41 Appendix A: Linear regression model and multiple regression model ...........................................42 Appendix B: ARIMA model ...........................................................................................................43 Appendix C: Predictions .................................................................................................................47 Appendix D: Correlation between regressors .................................................................................49 Appendix E: estimation results for models used to predict the regressors......................................51 Appendix F: Unit root test ..............................................................................................................53 References.......................................................................................................................................54 Figure 1: Equilibrium exchange rate...............................................................................................12 Figure 2: The plot of the monthly AUD/JPY exchange rate ...........................................................28 Figure 3: The plot of the average monthly exchange rate of AUD/JPY..........................................29 Figure 4: Time plot of the first difference.......................................................................................32 Figure 5: Autocorrelation function (AFC) ......................................................................................33 Figure 6: Partial autocorrelation function (PACF)..........................................................................34 Table 1: Correlation between AUD/JPY and the gold prices ..........................................................15 Table 2: Correlation between AUD/JPY and the oil price ..............................................................16 Table 3: Variable description...........................................................................................................23