FORECASTING ROL/USD EXCHANGE RATE USING ARTIFICIAL NEURAL NETWORKS. A COMPARISON WITH AN ECONOMETRIC MODEL.

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FORECASTING ROL/USD EXCHANGE RATE USING
ARTIFICIAL NEURAL NETWORKS. A COMPARISON WITH
AN ECONOMETRIC MODEL.
DOCTORAL SCHOOL OF FINANCE AND BANKING
DOFIN ACADEMY OF ECONOMIC STUDIES, BUCHAREST

• MSc. Student BÎRLÃ MARIUS
• Supervisor Phd. Professor MOISÃ ALTÃR

July, 2003
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1 OBJECTIVE
Compare the forecasts of the exchange rate
return, deriving from two specifications
An econometric model
An artificial neural network model
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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.

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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.

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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)
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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
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3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC
FUNDAMENTALS
Goods market
Real exchange rate
gtinflation rate
gtat 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.

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3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC
FUNDAMENTALS
p
PPP (45o)
p1
p0
s0
s1
sovershooting
s
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3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC
FUNDAMENTALS
C. The portfolio balance model
Investors portfolios
Investors wealth
W M B SB M1lt0, M2lt0 B1gt0, B2lt0 B1lt0, B2gt0
Money MM(i,iSe)
Domestic Bonds BB(i,iSe)
Foreign Bonds BB(i,iSe)
-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.
Se expected rate of depreciation of domestic
curency
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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.
?
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4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
The human neuron
Source Brown Benchmark IntroductoryPshychology
Electronic Image Bank, 1995. Times Mirror Higher
Education Group Inc.
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4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
The artificial neuron
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4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
Feedforward neural networks
Goal
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4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
The overfitting problem
A. Early stopping
Stop training when MSE(Validation sample) reaches
minimum.
B. Bayesian regularization
Goal
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
The equation
Where ?st the change in the real exchange
rate ?rt the change in the net international
reserves ?mt the change in the real money
supply (aggregate M2) ?et the change in the
exports to imports ratio pt the real index of
industrial production ?dt the change in the
interest rate pt 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 199201 200201
• Out-of-sample observations 200202 200301

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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
The regression of the linear model
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Tests for autocorrelation of the residuals
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Actual, fitted and residuals
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Static forecasting
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5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Dynamic forecasting
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Indicators of prediction accuracy
d)Bias proportion

1. 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
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN (1,6,1) (1,6,1) (1,7,1) (1,7,1) (1,8,1) (1,8,1) (1,9,1) (1,9,1) (1,10,1) (1,10,1)
  STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC
RMSE 0.02283 0.46145 0.023484 0.044229 0.026946 0.036525 0.042758 0.052129 0.023533 0.034926
MSE 0.018358 0.040794 0.018317 0.037117 0.022543 0.029114 0.030352 0.041264 0.019572 0.029723
MAPE 278.1927 822.6506 255.0829 742.3622 437.8635 663.2017 627.2425 1025.014 318.6407 650.8908
TIC 0.645949 0.803904 0.65728 0.798474 0.705611 0.777047 0.81208 0.836406 0.687194 0.765935
BIAS 0.190603 0.781521 0.181656 0.704427 0.065356 0.361525 0.00004 0.297564 0.071794 0.576338
VAR 0.243053 0.020014 0.247513 0.050937 0.351306 0.207646 0.567109 0.46349 0.257819 0.064934
COVAR 0.566344 0.198466 0.50831 0.244789 0.583339 0.430829 0.43285 0.238946 0.670387 0.358728
SIGN 0.5 0.666667 0.5 0.666667 0.416667 0.583333 0.333333 0.583333 0.416667 0.583333
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN (1,7,6,1) (1,7,6,1) (1,7,7,1) (1,7,7,1) (1,7,8,1) (1,7,8,1) (1,7,9,1) (1,7,9,1) (1,7,10,1) (1,7,10,1)
  STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC
RMSE 0.032014 0.040833 0.021634 0.036642 0.032745 0.043351 0.027759 0.037906 0.040599 0.040599
MSE 0.022744 0.027208 0.168 0.0299 0.023737 0.029152 0.020414 0.027429 0.027401 0.027401
MAPE 375.5224 579.8027 267.062 625.112 435.3916 541.5262 347.004 614.991 593.8604 593.8604
TIC 0.714484 0.786075 0.640472 0.774847 0.729064 0.807846 0.696667 0.784511 0.797833 0.797833
BIAS 0.060002 0.276366 0.168249 0.55064 0.018819 0.166218 0.099262 0.22859 0.263781 0.263781
VAR 0.501374 0.331118 0.217551 0.089272 0.525204 0.416178 0.374663 0.319403 0.310819 0.310819
COVAR 0.438624 0.392517 0.6142 0.360089 0.455976 0.417604 0.526075 0.452007 0.4254 0.4254
SIGN 0.416667 0.583333 0.416667 0.583333 0.5 0.583333 0.5 0.5 0.583333 0.583333
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN (1,7,7,6,1) (1,7,7,6,1) (1,7,7,7,1) (1,7,7,7,1) (1,7,7,8,1) (1,7,7,8,1) (1,7,7,9,1) (1,7,7,9,1) (1,7,7,10,1) (1,7,7,10,1)
  STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC STATIC DYNAMIC
RMSE 0.036063 0.064357 0.020234 0.019787 0.027899 0.031058 0.027793 0.032251 0.021931 0.05064
MSE 0.025199 0.049518 0.015532 0.015234 0.021914 0.02468 0.022097 0.024629 0.018555 0.045576
MAPE 463.1107 941.0469 349.023 430.1832 397.0747 534.129 450.443 609.054 362.5032 954.4723
TIC 0.708076 0.852817 0.634974 0.634972 0.704775 0.729059 0.665572 0.716331 0.62241 0.818536
BIAS 0.205139 0.592007 0.005931 0.132085 0.055268 0.424478 0.060647 0.531989 0.131289 0.809984
VAR 0.503397 0.191644 0.296461 0.16537 0.397364 0.152679 0.506848 0.139845 0.31299 0.015954
COVAR 0.291464 0.216349 0.697609 0.702545 0.547367 0.422843 0.432505 0.328167 0.555721 0.174062
SIGN 0.583333 0.666667 0.416667 0.583333 0.333333 0.583333 0.666667 0.666667 0.5 0.666667
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
  OLS OLS
  STATIC DYNAMIC
RMSE 0.033891 0.035179
MSE 0.023698 0.024348
MAPE 473.7145 481.4462
TIC 0.736203 0.739305
BIAS 0.057203 0.372823
VAR 0.561383 0.4087
COVAR 0.381413 0.218477
SIGN 0.666667 0.75
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
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Results
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Results
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Results
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Results
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Results
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Results
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
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Results
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Results
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Results
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Results
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Results
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Results
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Results
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Results
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Conclusion

• ANN performs better than OLS in static
  forecasting, in most of the configurations
• OLS performs better in dynamic forecasting in
  most of the cases, except for ANN(1,7,7,7,1)
• OLS predicts better the correct sign of excess
  returns.

Shortcomings of ANN model
-An important drawback is represented by the fact
that there is no rule for designing ANNs. This is
an empirical process of trial and error, through
which one adds and removes hidden layers and/or
neural units from the structure of the network
until a minimum value for the loss function is
reached. This process is time consuming and
requires considerable computing resources.
Another limitation is the small number of
benchmark models necessary to assessing the
predictive power of the network. For further
research one can consider more than one
econometric model and a larger battery of tests
and indicators in order to achieve a better
comparison between the models.