Haiqin Yang, Irwin King and Laiwan Chan Department of Computer Science and Engineering
description
Transcript of Haiqin Yang, Irwin King and Laiwan Chan Department of Computer Science and Engineering
Non-fixed and Asymmetrical Margin Approach to Stock Market
Prediction using Support Vector Regression
Haiqin Yang, Irwin King and Laiwan ChanDepartment of Computer Science and Engineering
The Chinese University of Hong Kong
November 18-22, 2002ICONIP’02
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Index
Motivation
SVR Introduction Approach
Conclusion
Experiments & Results
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Motivation
Combine them:
Non-fixed and Asymmetrical margin
Two characteristics: fixed and symmetrical
Predictive accuracy only?
Downside risk!
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Support Vector Regreesion (SVR) introduction Developed by Vapnik (1995)Developed by Vapnik (1995)
Model:Model:
estimate objective function:estimate objective function:
minimizeminimize
train data:train data:
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SVR Introduction (Cont’d)
Loss function:
The objective function f is represented by the dotted points.
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Related Applications
Support Vector Method for Function Approximation, Support Vector Method for Function Approximation, Regression Estimation and Signal Processing (VapniRegression Estimation and Signal Processing (Vapnik et al., 1996)k et al., 1996)
Predicting time series with support vector machine Predicting time series with support vector machine (Muller et al., 1997)(Muller et al., 1997)
Application of support vector machines to financial tiApplication of support vector machines to financial time series forecasting (E.H.Tay and L.J.Cao. 2001)me series forecasting (E.H.Tay and L.J.Cao. 2001)
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Approach
Two characteristics: 4 kinds of margins
SSymmetricalymmetrical AsymmetricalAsymmetrical
FFixedixed
Non-fixedNon-fixed
fixed,
symmetrical.
FASMFASM
NASMNASM
FAAMFAAM
NAAMNAAM
+ + + + + + + + + +
+ + + + + + + + + +
+ + + + + + + + + +
+ + + + + + + + + +
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Previous setting
Previous others’ method
SSymmetricalymmetrical AsymmetricalAsymmetrical
FFixedixed
Non-fixedNon-fixed
SSymmetricalymmetrical AsymmetricalAsymmetrical
FFixedixed FASMFASM FAAMFAAM
Non-fixedNon-fixed NASMNASM NAAMNAAM
In our previous work: Support Vector Machines Regression for volatile stock market prediction (IDEAL’02)
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New Approach
Two characteristics of the margin in
– insensitive loss function: fixed and symmetrical.
Non-fixedNon-fixed
AsymmetricalAsymmetricalSSymmetricalymmetrical
FFixedixed
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Formulas A general type of –Insensitive loss function
Fixed and Symmetrical Margin (FASM):
Fixed and Asymmetrical Margin (FAAM):
Non-fixed and Symmetrical Margin (NASM):
Non-fixed and Asymmetrical Margin (NAAM):
up margin
down margin
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Formulas
QP problem:
s.t. Objective function:
Kernel function:
e.g. RBF
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How to set margin?
Margin width:Up margin:Down margin:
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Experiment
Accuracy Metrics• MAE:
• UMAE:
• DMAE:
• actual value,
• predictive value
• number of testing data
m
iii pa
m 1
||1
m
paiii
ii
pam ,1
)(1
m
paiii
ii
apm ,1
)(1
iaipm
Total error
Upside risk
Downside risk
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Experiment Description
Model: Data: Hang Seng Index (HSI),
Dow Jones Industrial Average (DJIA). Time periods: Jan. 2, 1998 ~ Dec. 29, 2000 (3 years) Ratio of training data and testing data: 5:1. Procedures: one day ahead prediction. Environments
• CPU: Pentium 4, 1.4 G
• Memory: RAM 512M
• OS: Windows2000
• Time: few hours.
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Experiment Description
Three kinds of experiments• Test the effect of parameters in NAAM to obtain a
better result.
• Compare the result of NAAM with NASM, AR(4), RBF network (also test the effect of the number of hidden units).
• Compare the results of NAAM, NASM with FASM and FAAM.
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Actual Parameter Setting
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Effect of Length of EMA in NAAM
HSI
222. 43 218. 18 217. 93 216. 5
0
50
100
150
200
250
MAEUMAEDMAE
Err
or
DJIA
85. 68 84. 12 84. 57 84. 8
0
20
40
60
80
100
MAEUMAEDMAE
Err
or
1,1,2
121 k
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Graphes HSI DJIA
Data Set
ratio
HSI 100 182.28
20.80 0.114
DJIA 30 79.95 15.64 0.196
n
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Effect of in NAAM
HSI )100( n
216. 5 216. 55 216. 19 216. 41
0
50
100
150
200
250
MAEUMAEDMAE
Err
or
DJIA
84. 12 84. 88 85. 02 85. 22
0
20
40
60
80
100
MAEUMAEDMAE
Err
or
)30( n
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Effect of kk in NAAM
HSI
216. 5 219. 02 228. 25
260. 73
0
50
100
150
200
250
300
MAEUMAEDMAE
Err
or
DJIA
84. 12 85. 4290. 99
103. 77
0
20
40
60
80
100
120
MAEUMAEDMAE
Err
or
)30( n)100( n
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Comparison Results
HSI
1,1,2
121 k
)100( n
216. 5
113. 04 103. 46
0
50
100
150
200
250
MAE UMAE DMAE
NAAMNASMAR(4)RBF(7)
Err
or
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Results
DJIA
1,1,2
121 k
)30( n85. 33
40. 2945. 04
0
10
20
30
40
50
60
70
80
90
MAE UMAE DMAE
NAAMNASMAR(4)RBF(9)
Err
or
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NAAM, NASM vs. FASM, FAAM
Fixed Margin: HSI
200)()( ii xuxd
)100( n
216. 5
113. 04 103. 46
0
50
100
150
200
250
MAE UMAE DMAE
NAAMNASMFi xed Margi n1Fi xed Margi n2Fi xed Margi n3Fi xed Margi n4Fi xed Margi n5Fi xed Margi n6Fi xed Margi n7Fi xed Margi n8Fi xed Margi n9Fi xed Margi n10Fi xed Margi n11
Err
or
Step: 20
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NAAM, NASM vs. FASM, FAAM
Fixed Margin: DJIA
90)()( ii xuxd
)30( n
84. 12
41. 13 42. 3
0102030405060708090
100
MAE UMAE DMAE
NAAMNASMFi xed Margi n1Fi xed Margi n2Fi xed Margi n3Fi xed Margi n4Fi xed Margi n5Fi xed Margi n6Fi xed Margi n7Fi xed Margi n8Fi xed Margi n9Fi xed Margi n10Fi xed Margi n11
Err
or
Step: 9
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Conclusion Propose non-fixed and asymmetrical margin (NAAM)
approach in SVR to predict stock market.
Compare this method to non-fixed symmetrical margin (NASM) approach, AR(4), RBF network.
NAAM, NASM outperform AR(4), RBF network.
NAAM can reduce the downside risk.
NAAM, NASM outperform FASM, FAAM.