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

2/25

Index

Motivation

SVR Introduction Approach

Conclusion

Experiments & Results

3/25

Motivation

Combine them:

Non-fixed and Asymmetrical margin

Two characteristics: fixed and symmetrical

Predictive accuracy only?

Downside risk!

4/25

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:

5/25

SVR Introduction (Cont’d)

Loss function:

The objective function f is represented by the dotted points.

6/25

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)

7/25

Approach

Two characteristics: 4 kinds of margins

SSymmetricalymmetrical AsymmetricalAsymmetrical

FFixedixed

Non-fixedNon-fixed

fixed,

symmetrical.

FASMFASM

NASMNASM

FAAMFAAM

NAAMNAAM

+ + + + + + + + + +

+ + + + + + + + + +

+ + + + + + + + + +

+ + + + + + + + + +

8/25

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)

9/25

New Approach

Two characteristics of the margin in

– insensitive loss function: fixed and symmetrical.

Non-fixedNon-fixed

AsymmetricalAsymmetricalSSymmetricalymmetrical

FFixedixed

10/25

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

11/25

Formulas

QP problem:

s.t. Objective function:

Kernel function:

e.g. RBF

12/25

How to set margin?

Margin width:Up margin:Down margin:

13/25

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

14/25

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.

15/25

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.

16/25

Actual Parameter Setting

17/25

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

18/25

Graphes HSI DJIA

Data Set

ratio

HSI 100 182.28

20.80 0.114

DJIA 30 79.95 15.64 0.196

n

19/25

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

20/25

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

21/25

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

22/25

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

23/25

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

24/25

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

25/25

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.