M S c. Student: BÎRLÃ MARIUS Supervisor: Phd. Professor MOISÃ ALTÃR

1. DOCTORAL SCHOOL OF FINANCE AND BANKING DOFIN ACADEMY OF ECONOMIC STUDIES, BUCHAREST FORECASTING ROL/USD EXCHANGE RATEUSING ARTIFICIAL NEURAL NETWORKS.A COMPARISON WITHAN ECONOMETRIC MODEL. MSc. Student: BÎRLÃ MARIUS Supervisor: Phd. Professor MOISÃ ALTÃR July, 2003

2. 1 OBJECTIVE Compare the forecasts of the exchange rate return, deriving from two specifications: An econometric model An artificial neural network model

3. 2 LITERATURE REVIEW • Kuan and Liu (1995) estimate and select feedforward and recurrent networks to evaluate their forecasting performance in case of five exchange rates against USD. The networks performed differently for different exchange rate series: • - for the japanese yen and british pound some selected networks have significant market timing ability (sign predictions) and significantly lower out-of-sample MPSE (mean squared prediction errors) relative to the random walk model in different testing periods; • - for the Canadian dollar and deutsche mark the selected networks exhibit only mediocre performance. • Plasmans, Weeren and Dumortier (1997) construct a neural network error correction model for the yen/dollar, pound/dollar and DM/dollar exchange rates that significantly outperforms both the random walk model and a linear vector error correction model. • Yao and Tan (2000) show that if technical indicators and time series data are fed to neural networks to capture the underlying rules of the movement in currency exchange rates then useful prediction can be made and significant paper profit can be achieved for out-of-sample data. Compared with an ARIMA model, this network performed better, standing for a viable alternative forecasting tool for the yen/dollar, DM/dollar, pound/dollar, Swiss franc/dollar and Australian dollar/dollar exchange rates.

4. 2 LITERATURE REVIEW • Gradojevic and Yang (2000) construct a neural network that never performs worse than a linear model embedding a set of macroeconomic variables (interest rate and crude oil price) and a variable from the field of microstructure (order flow), but always performs better than the random walk model when predicting Canadian dollar/dollar exchange rate; • Qi and Wu (2002) use a neural network in order to make forecasts for the yen/dollar, DM/dollar, Australian dollar/dollar and pound/dollar exchange rates movements. The network is fed with data series concerning the following macroeconomic fundamentals: the money supply M1, the real industrial production and the interest rate. The network cannot outperform the random walk model for the out-of-sample forecast especially if the prediction horizon increases. The study suggest that neither the non-linearity, nor market fundamentals seems to play a very important role in improving the forecasts for the chosen horizons.

5. 3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS A. The monetary model – flexible prices The real income (y) The demand for money (m) The nominal interest rate (i) The price level (p) Monetary equilibria: (1) Purchasing power parity condition: (2) st – exchange rate (3)

6. 3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS B. The monetary model – sticky prices • Assumptions: • perfect mobility of the capital; • instant adjustment of the monetary market; • sticky prices; • perfect foresights of the exchange rate. expected appreciation / depreciation of the exchange rate Uncovered interest rate parity condition: Monetary market:

7. 3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS Goods market: Real exchange rate >inflation rate: >at equilibrium, when • In long-run, an increase in money supply has no real effect on prices and exchange rate. • In short-run (due to stickiness of the prices), a monetary expansion has real effects on economy.

8. 3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS p PPP (45o) p1 p0 s0 s1 sovershooting s

9. 3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS C. The portfolio balance model Investors’ portfolios: Investors’ wealth: W = M + B + SB* M1<0, M2<0 B1>0, B2<0 B1<0, B2>0 Money M=M(i,i*+Ŝe) Domestic Bonds B=B(i,i*+Ŝe) Foreign Bonds B*=B*(i,i*+Ŝe) -When bondholders will buy domestic bonds to hedge their portfolios the domestic interest rates will get lower, causing an increase in value of domestic currency. Ŝe – expected rate of depreciation of domestic curency

10. 3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS D. The market information approach When a significant event is expected to occur, action is taken in present rather than delayed. Inflation is expected to rise The currency will devalue in anticipation of the event. →

11. 4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK The human neuron Source: Brown & Benchmark IntroductoryPshychology Electronic Image Bank, 1995. Times Mirror Higher Education Group Inc.

12. 4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK The artificial neuron

13. 4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK Feedforward neural networks Goal:

14. 4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK The overfitting problem A. Early stopping Stop training when MSE(Validation sample) reaches minimum. B. Bayesian regularization Goal:

15. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN The equation Where Δst – the change in the real exchange rate; Δrt – the change in the net international reserves; Δmt – the change in the real money supply (aggregate M2); Δet – the change in the exports to imports ratio; pt – the real index of industrial production; Δdt – the change in the interest rate; πt – the inflation rate.  All variables, except the absolute change in the net international reserves and the interest rate change, are expressed in logarithms. • In-sample observations: 1992:01 – 2002:01 • Out-of-sample observations: 2002:02 – 2003:01

16. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Unit root tests

17. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Unit root tests

18. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Unit root tests

19. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Unit root tests

20. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Unit root tests

21. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Unit root tests

22. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN The regression of the linear model

23. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Tests for autocorrelation of the residuals

24. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Actual, fitted and residuals

25. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Static forecasting

26. 5 A LINEAR MODEL OF EXCHANGE RATE RETURN Dynamic forecasting

27. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Indicators of prediction accuracy d)Bias proportion • Root mean square error (RMSE) b)Mean absolute error (MAE) e)Variance proportion c)Mean absolute percentage error (MAPE) f)Covariance proportion d)Theil inequality coefficient (TIC) g)The sign test where

28. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

29. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

30. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

31. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

32. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

33. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

34. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

35. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

36. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

37. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

38. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

39. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

40. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

41. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

42. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

43. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

44. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

45. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

46. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

47. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results

48. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results ANN (1,7,7,7,1)

49. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results ANN (1,7,7,7,1)

50. 6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION Results ANN (1,7,7,7,1)