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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. M S c. Student: BÎRLÃ MARIUS Supervisor: Phd. Professor MOISÃ ALTÃR. July, 2003. 1 OBJECTIVE. - PowerPoint PPT Presentation
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FORECASTING ROL/USD EXCHANGE RATEFORECASTING ROL/USD EXCHANGE RATE USINGUSING
ARTIFICIAL NEURAL NETWORKS. ARTIFICIAL NEURAL NETWORKS.
A COMPARISON WITHA COMPARISON WITH AN ECONOMETRIC MODEL.AN ECONOMETRIC MODEL.
MMSSc. Student: BÎRLÃ MARIUSc. Student: BÎRLÃ MARIUSSupervisor: Phd. Professor MOISÃ ALTÃRSupervisor: Phd. Professor MOISÃ ALTÃR
DOCTORAL SCHOOL OF FINANCE AND BANKING DOFIN
ACADEMY OF ECONOMIC STUDIES, BUCHAREST
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 demandfor money
(m)
The nominalinterest rate
(i)
The real income(y)
The price level(p)
Monetary equilibria:
Purchasing power parity condition:*ttt pps
st – exchange rate
*****ttttttt iiykkymms
(1)
(2)
(3)
B. The monetary model – sticky prices
3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS
Assumptions:• perfect mobility of the capital;• instant adjustment of the monetary market;• sticky prices;• perfect foresights of the exchange rate.
Uncovered interest rate parity condition:
)(* ssii
)(
)(*
*
yimp
ssiypm
iypm
expected appreciation / depreciation of the exchange rate
Monetary market:
)(1 ppss
Goods market:
3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS
)( psiyy SD
)]()1[()(
peiypyyp SD
:0 *iiandp
Real exchange rate
>inflation rate:
>at equilibrium, when
])1[(1 *iyps
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
s0 s1 sovershooting
p0
p1
p
s
PPP (45o)
C. The portfolio balance model
3 EXCHANGE RATE MOVEMENTS AND MACROECONOMIC FUNDAMENTALS
Investors’ portfolios:
MoneyM=M(i,i*+Ŝe)
Domestic BondsB=B(i,i*+Ŝe)
Foreign BondsB*=B*(i,i*+Ŝe)
Investors’ wealth:
W = M + B + SB*
M1<0, M2<0
B1>0, B2<0
B1<0, B2>0
Ŝe – expected rate of depreciation of domestic curency
-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.
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 xexf
11)(
)()()( xx
xx
eeeexf
Goal: )][1min()1min()min(1
2
1
2
S
ttt
S
tt ay
SSMSE
4 ARTIFICIAL NEURAL NETWORKS FRAMEWORK
The overfitting problem
A. Early stopping
Stop training when MSE(Validation sample) reaches minimum.
B. Bayesian regularization
ratioeperformancbiasesandweightsofnumbern
wMSW
whereMSWMSEMSEREG
n
tj
,
))1(min()min(
1
2Goal:
5 A LINEAR MODEL OF EXCHANGE RATE RETURN
ttttttttt dcpcecmcrcsccs )(65432110
WhereΔst – 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
The equation
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)
hT
Tttt yy
hRMSE
1
2)ˆ(1
b)Mean absolute error (MAE)
hT
Tttt yy
hMAE
1
ˆ1
c)Mean absolute percentage error (MAPE)
hT
Tt t
tt
yyy
hMAPE
1
ˆ1100
d)Theil inequality coefficient (TIC)
hT
Ttt
hT
Ttt
hT
Tttt
yh
yh
yyhTIC
1
2
1
2
1
2
1ˆ1
)ˆ(1
d)Bias proportion
hyyyhy
BIAStt
t
/)ˆ())/ˆ((
2
2
e)Variance proportion
hyy
ssPROPVAR
tt
yy
/)ˆ()(
.. 2
2ˆ
f)Covariance proportion
hyy
ssrPROPCOV
tt
yy
/)ˆ()1(2
.. 2ˆ
g)The sign test
hT
TttdIS
1
)(
where
ttt
tt
yydotherwisedif
dI
ˆ,0
0,1)(
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN (1,6,1) (1,7,1) (1,8,1) (1,9,1) (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
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN (1,7,6,1) (1,7,7,1) (1,7,8,1) (1,7,9,1) (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
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
ANN (1,7,7,6,1) (1,7,7,7,1) (1,7,7,8,1) (1,7,7,9,1) (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
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
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
RMSE - Static forecasting
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Type on ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MSE - Static forecasting
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MAPE - Static forecasting
0
100
200
300
400
500
600
700
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
TIC - Static forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
BIAS PROPORTION - Static forecasting
0
0.05
0.1
0.15
0.2
0.25
0.3
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
VARIANCE PROPORTION - Static forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
COVARIANCE PROPORTION - Static forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
SIGN TEST - Static forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
RMSE - Dynamic forecasting
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Type on ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MSE - Dynamic forecasting
0
0.01
0.02
0.03
0.04
0.05
0.06
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
MAPE - Dynamic forecasting
0
200
400
600
800
1000
1200
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
TIC - Static forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
BIAS PROPORTION - Dynamic forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
VARIANCE PROPORTION - Dynamic forecasting
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
COVARIANCE PROPORTION - Dynamic forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Type of ANN
ANN
OLS
6 NEURAL NETWORK TRAINING AND FORECAST EVALUATION
Results
SIGN TEST - Dynamic forecasting
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Type of ANN
ANN
OLS
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.
-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.
Shortcomings of ANN model