DOCTORAL SCHOOL OF FINANCE AND BANKING DOFIN
ACADEMY OF ECONOMIC STUDIES, BUCHAREST
FORECASTING ROL/USD EXCHANGE RATE USING
ARTIFICIAL NEURAL NETWORKS.
A COMPARISON WITH AN ECONOMETRIC MODEL.
MSc. Student: BÎRLÃ MARIUS
Supervisor: Phd. Professor MOISÃ ALTÃR
July, 2003
1 OBJECTIVE
Compare the forecasts of the exchange rate return, deriving from two specifications:
An econometric model
An artificial neural network model
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.
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.
3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS
A. The monetary model – flexible prices
The real income
(y)
The demand
for money
(m)
The price level
(p)
The nominal
interest rate
(i)
Monetary equilibria:
(1)
Purchasing power parity condition:
st  pt  pt*
(2)
st – exchange rate
 st  mt  mt*  kyt  k * yt*  it   *it*
(3)
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:
i  i *   ( s  s)
Monetary market:
m  p  y  i
 m  p  y  i *   ( s  s)
 p  m  (i *  y )
ss
1

( p  p)
3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS
Goods market:
y D  y S  i   (s  p)
Real exchange
rate
>inflation rate:
p   ( y D  y S )
 p   [(  1) y  i   (e  p)]
>at equilibrium, when
p  0 and i  i* :
1
s  p  [(1   ) y  i * ]

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.
3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS
p
PPP (45o)
p1
p0
s0
s1
sovershooting
s
3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS
C. The portfolio balance model
Investors’ portfolios:
Money
M=M(i,i*+Ŝe)
Domestic Bonds
B=B(i,i*+Ŝe)
Foreign Bonds
B*=B*(i,i*+Ŝe)
Investors’ wealth:
W = M + B + SB*
M1<0, M2<0
B1>0, B2<0
B1<0, B2>0
-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
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.
4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
The human neuron
Source: Brown & Benchmark IntroductoryPshychology Electronic Image
Bank, 1995. Times Mirror Higher Education Group Inc.
4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
The artificial neuron
4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
Feedforward neural networks
f ( x) 
1
1  ex
(e x  e  x )
f ( x)  x  x
(e  e )
1 S 2
1 S
Goal: min( MSE )  min(   t )  min(  [ yt  at ]2 )
S t 1
S t 1
4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
The overfitting problem
A. Early stopping
Stop training when MSE(Validation sample) reaches minimum.
B. Bayesian regularization
min( MSEREG )  min(   MSE  (1   )  MSW )
where
n
Goal:
MSW   w2j ,
t 1
n  number of weights and biases
  performance ratio
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
The equation
st  c0  c1st 1  c2 rt  c3mt  c4 et  c5 pt  c6 (dt   t )   t
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
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Unit root tests
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
The regression of the linear model
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Tests for autocorrelation of the residuals
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Actual, fitted and residuals
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Static forecasting
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
Dynamic forecasting
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Indicators of prediction accuracy
a)Root mean square error (RMSE)
RMSE 
1 T h
( yˆt  yt ) 2

h t T 1
d)Bias proportion
BIAS 
(( yˆt / h)  y ) 2
 ( yˆt  yt )2 / h
b)Mean absolute error (MAE)
e)Variance proportion
MAE 
1 T h
 yˆt  yt
h t T 1
VAR.PROP . 
c)Mean absolute percentage error (MAPE)
( s yˆ  s y ) 2
 ( yˆt  yt )2 / h
f)Covariance proportion
1 T h yˆt  yt
MAPE  100 
h t T 1 yt
COV .PROP . 
2(1  r ) s yˆ s y
 ( yˆt  yt )2 / h
d)Theil inequality coefficient (TIC)
g)The sign test
TIC 
1 T h
( yˆ t  yt ) 2

h t T 1
1 T h 2
1 T h 2
yˆ t 

 yt
h t T 1
h t T 1
S
T h
I
t T 1

(d t )
where
 1, if d t  0
I  (d t )  
0, otherwise
d t  yˆ t yt
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN
(1,6,1)
STATIC
RMSE
(1,7,1)
DYNAMIC
STATIC
DYNAMIC
(1,8,1)
STATIC
DYNAMIC
(1,9,1)
STATIC
(1,10,1)
DYNAMIC
STATIC
DYNAMIC
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
0.5
0.666667
0.5
0.666667
0.416667
0.583333
0.333333
0.583333
0.416667
0.583333
SIGN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN
(1,7,6,1)
STATIC
DYNAMIC
(1,7,7,1)
STATIC
(1,7,8,1)
DYNAMIC
STATIC
DYNAMIC
(1,7,9,1)
STATIC
(1,7,10,1)
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
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN
(1,7,7,6,1)
STATIC
DYNAMIC
(1,7,7,7,1)
STATIC
DYNAMIC
(1,7,7,8,1)
STATIC
DYNAMIC
(1,7,7,9,1)
STATIC
DYNAMIC
(1,7,7,10,1)
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
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
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
RMSE - Static forecasting
0.045
0.04
0.035
0.03
0.025
ANN
0.02
OLS
0.015
0.01
0.005
0
Type on ANN
(1
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(1
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MSE - Static forecasting
0.035
0.03
0.025
0.02
ANN
0.015
OLS
0.01
0.005
0
Type of ANN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MAPE - Static forecasting
700
600
500
400
ANN
300
OLS
200
100
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
TIC - Static forecasting
0.9
0.8
0.7
0.6
0.5
ANN
0.4
OLS
0.3
0.2
0.1
0
Type of ANN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
BIAS PROPORTION - Static forecasting
0.3
0.25
0.2
ANN
0.15
OLS
0.1
0.05
0
(1
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Type of ANN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
VARIANCE PROPORTION - Static forecasting
0.6
0.5
0.4
ANN
0.3
OLS
0.2
0.1
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Type of ANN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
COVARIANCE PROPORTION - Static forecasting
0.8
0.7
0.6
0.5
ANN
0.4
OLS
0.3
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6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
SIGN TEST - Static forecasting
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(1
(1
(1
(1
(1
(1
Type of ANN
(1
,6
,1
)
(1
,7
,1
)
(1
,8
,1
)
(1
,9
,1
)
(1
,1
0,
1)
(1
,7
,6
,
(1 1)
,7
,7
,
(1 1)
,7
,8
,
(1 1)
,7
,9
,1
(1
)
,7
,1
(1 0 ,1
)
,7
,7
,6
,1
(1
)
,7
,7
,
(1 7,1
)
,7
,7
,
(1 8,1
)
,7
,7
,9
(1
,1
,7
)
,7
,1
0,
1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
RMSE - Dynamic forecasting
0.07
0.06
0.05
0.04
ANN
0.03
OLS
0.02
0.01
0
Type on ANN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MSE - Dynamic forecasting
0.06
0.05
0.04
ANN
0.03
OLS
0.02
0.01
0
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
,1
,1 6,1
,1
,1
,1
,1
,1
,1
,1
,1
,1
,1
,1
,1
6
7
8
9
0
6
7
8
9
0
7
8
9
0
,
,
,
,
,
,
,
,
,
,
,
,
,1
,1
,1
,7
,7
,7
,7
(1
(1
(1
(1
,7
,7
,7
,7
7
7
,
(1
1
1
1
1
7
7
7
7
,
,
,
,
,
(
(
(
(
,7
(1
(1
(1
(1
(1
(1
Type of ANN
(1
,6
,1
)
(1
,7
,1
)
(1
,8
,1
)
(1
,9
,1
)
(1
,1
0,
1)
(1
,7
,6
,
(1 1)
,7
,7
,
(1 1)
,7
,8
,
(1 1)
,7
,9
,1
(1
)
,7
,1
(1 0 ,1
)
,7
,7
,
(1 6,1
)
,7
,7
,
(1 7,1
)
,7
,7
,
(1 8,1
)
,7
,7
,9
(1
,1
,7
)
,7
,1
0,
1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MAPE - Dynamic forecasting
1200
1000
800
600
ANN
OLS
400
200
0
Type of ANN
(1
,6
,1
)
(1
,7
,1
)
(1
,8
,1
)
(1
,9
,1
)
(1
,1
0,
1)
(1
,7
,6
,1
)
(1
,7
,7
,1
)
(1
,7
,8
,
(1 1)
,7
,9
,1
(1
)
,7
,1
(1 0 ,1
)
,7
,7
,6
,1
(1
)
,7
,7
,7
,1
(1
)
,7
,7
,
(1 8,1
)
,7
,7
,9
(1
,1
,7
)
,7
,1
0,
1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
TIC - Static forecasting
0.9
0.8
0.7
0.6
0.5
ANN
0.4
OLS
0.3
0.2
0.1
0
Type of ANN
(1
,6
,1
)
(1
,7
,1
)
(1
,8
,1
)
(1
,9
,1
)
(1
,1
0,
1)
(1
,7
,6
,1
)
(1
,7
,7
,1
)
(1
,7
,8
,
(1 1)
,7
,9
,1
(1
)
,7
,1
(1 0 ,1
)
,7
,7
,6
,1
(1
)
,7
,7
,7
,1
(1
)
,7
,7
,
(1 8,1
)
,7
,7
,9
(1
,1
,7
)
,7
,1
0,
1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
BIAS PROPORTION - Dynamic forecasting
0.9
0.8
0.7
0.6
0.5
ANN
0.4
OLS
0.3
0.2
0.1
0
Type of ANN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
VARIANCE PROPORTION - Dynamic forecasting
0.5
0.45
0.4
0.35
0.3
ANN
0.25
OLS
0.2
0.15
0.1
0.05
(1
,6
,1
)
(1
,7
,1
)
(1
,8
,1
)
(1
,9
,1
)
(1
,1
0,
1)
(1
,7
,6
,
(1 1)
,7
,7
,
(1 1)
,7
,8
,
(1 1)
,7
,9
,1
(1
)
,7
,1
(1 0 ,1
)
,7
,7
,6
,1
(1
)
,7
,7
,
(1 7,1
)
,7
,7
,
(1 8,1
)
,7
,7
,9
(1
,1
,7
)
,7
,1
0,
1)
0
Type of ANN
(1
,6
,1
)
(1
,7
,1
)
(1
,8
,1
)
(1
,9
,1
)
(1
,1
0,
1)
(1
,7
,6
,1
)
(1
,7
,7
,1
)
(1
,7
,8
,
(1 1)
,7
,9
,1
(1
)
,7
,1
(1 0 ,1
)
,7
,7
,6
,1
(1
)
,7
,7
,7
,1
(1
)
,7
,7
,
(1 8,1
)
,7
,7
,9
(1
,1
,7
)
,7
,1
0,
1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
COVARIANCE PROPORTION - Dynamic forecasting
0.8
0.7
0.6
0.5
0.4
ANN
OLS
0.3
0.2
0.1
0
Type of ANN
(1
,6
,1
)
(1
,7
,1
)
(1
,8
,1
)
(1
,9
,1
)
(1
,1
0,
1)
(1
,7
,6
,1
)
(1
,7
,7
,1
)
(1
,7
,8
,
(1 1)
,7
,9
,1
(1
)
,7
,1
(1 0 ,1
)
,7
,7
,6
,1
(1
)
,7
,7
,7
,1
(1
)
,7
,7
,
(1 8,1
)
,7
,7
,9
(1
,1
,7
)
,7
,1
0,
1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
SIGN TEST - Dynamic forecasting
0.8
0.7
0.6
0.5
0.4
ANN
OLS
0.3
0.2
0.1
0
Type of ANN
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results ANN (1,7,7,7,1)
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.