m s c. student: bÎrlÃ marius supervisor: phd. professor moisÃ altÃr

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


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:


)( psiyy SD

)]()1[(

)(

peiyp

yyp 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.


s0 s1 sovershooting

p0

p1

p

s

PPP (45o)

C. The portfolio balance model


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.


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.


The artificial neuron


Feedforward neural networks xexf

1

1)(

)(

)()(

xx

xx

ee

eexf

Goal: )][1

min()1

min()min(1

2

1

2

S

ttt

S

tt ay

SSMSE


The overfitting problem

A. Early stopping

Stop training when MSE(Validation sample) reaches minimum.

B. Bayesian regularization

ratioeperformanc

biasesandweightsofnumbern

wMSW

where

MSWMSEMSEREG

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


Unit root tests


The regression of the linear model


Tests for autocorrelation of the residuals


Actual, fitted and residuals


Static forecasting


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

y

yy

hMAPE

1

ˆ1100

d)Theil inequality coefficient (TIC)

hT

Ttt

hT

Ttt

hT

Tttt

yh

yh

yyh

TIC

1

2

1

2

1

2

1ˆ

1

)ˆ(1

d)Bias proportion

hyy

yhyBIAS

tt

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..

2

ˆ

g)The sign test

hT

TttdIS

1

)(

where

ttt

tt

yyd

otherwise

difdI

ˆ

,0

0,1)(


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


Results

ANN (1,7,6,1) (1,7,7,1) (1,7,8,1) (1,7,9,1) (1,7,10,1)


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


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)


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


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


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


Results

MSE - Static forecasting

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Type of ANN

ANN

OLS


Results

MAPE - Static forecasting

0

100

200

300

400

500

600

700

Type of ANN

ANN

OLS


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


Results

BIAS PROPORTION - Static forecasting

0

0.05

0.1

0.15

0.2

0.25

0.3

Type of ANN

ANN

OLS


Results

VARIANCE PROPORTION - Static forecasting

0

0.1

0.2

0.3

0.4

0.5

0.6

Type of ANN

ANN

OLS


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


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


Results

RMSE - Dynamic forecasting

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Type on ANN

ANN

OLS


Results

MSE - Dynamic forecasting

0

0.01

0.02

0.03

0.04

0.05

0.06

Type of ANN

ANN

OLS


Results

MAPE - Dynamic forecasting

0

200

400

600

800

1000

1200

Type of ANN

ANN

OLS


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


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


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


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


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


Results ANN (1,7,7,7,1)


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

m s c. student: bÎrlÃ marius supervisor: phd. professor moisÃ altÃr

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