A Hybrid ARIMA and Support Vector Machines Model in
Stock Price Forecasting
Ping-Feng Pai, Chih-Sheng Lin
The International Journal of Management Science
2004
Fanghua Lin
Financial Services Analytics, UD
Content
• Models
• ARIMA
• SVM
• Hybrid Model
• Empirical Results
• Conclusion
• Start-up
Traditional Finance Model in Forecasting: ARIMA
𝑦𝑡 : Stock Price at time t
𝑝
𝑦𝑡 = 𝜃0 +
𝑞
∅i 𝑦𝑡−i +
𝑖=1
𝜃j 𝜀𝑡−j + 𝜀𝑡
𝑗=1
i.e.,
Future Value = 𝑓(Past Values, Past Errors)
• Data-oriented approach: sensitive to data structure
• Linear , cannot catch the non-linear part
SVM
SVM
Non-linearly separable functions
Linearly separable function
Kernel functions
In this paper, The Gaussian kernel function is used
Hybrid Model: ARIMA & SVM
𝑍𝑡 = 𝑌𝑡
+ 𝑁𝑡
Linear part Nonlinear part
Data
Residuals
ARIMA
𝑌𝑡
SVM
+
𝑁𝑡
= 𝑍𝑡
Empirical Study
Data
Daily Stock Closing Price （eg. General Motors Corporation）
Stocks
10 stocks
Time Period
10/21/2002 - 2/28/2003
Data Set Split
Training dataset
Validation data set
Testing data set
10/21/2002 -12/31/2012
1/2/2003-1/31/2003
2/3/2003-2/28/2003
Goal Comparision
Model 1: ARIMA(0,1,0)
Model 2: SVM
Model 3: ARIMA + SVM
Forecasting Accuracy
Model 4: Hybrid Model
MAE(mean absolute error), MSE(mean square error), MAPE (mean
absolute percent error), RMSE (root mean square error)
Different Parameters for Ten Stocks
SVMs models
ARIMA models
(0,1,0)
Eastman Kodak Company
(0,1,0)
General Motors Corporation
(0,1,0)
J.P.Morgan Chanse & Co.
(0,1,0)
Altria Group, Inc.
(0,1,0)
SBC
(0,1,0)
Citigroup Inc.
(0,1,0)
General Electirc Company
(0,1,0)
Southwest Water Company
(0,1,0)
American National Insurance Company
ATP Oil & Gas Corporation
s
0.3
1.9
1.3
1.3
1.5
0.6
0.6
1.7
1.4
1.2
σ
0
0.3
0
0
0.1
0
0.4
0
0
0
C
100
100
100
100
100
100
100
100
100
100
Hybrid models
s
1.0
3.4
2.0
4.1
4.2
1.0
3.2
0.3
0.7
2.0
σ
0.2
0
0
0
0
0.1
0.4
0.4
0.8
0.2
C
10
1
1
1
1
10
10
10
10
10
Results
Results
Model 1: ARIMA(0,1,0)
Model 2: SVM
Model 3: ARIMA +SVM
Model 4: Hybrid Model
MAE
0.4905
0.4352
0.4586
0.2579
MSE
0.3748
0.3186
0.3569
0.2049
Hybrid Model performs the best
MAPE
1.4214
1.2654
1.3391
0.7550
RMSE
0.6122
0.5644
0.5974
0.3162
Conclusion
•
Simple combination of ARIMA and SVM does not perform better than ARIMA model or
SVM model
•
Hybrid Model of ARIMA and SVM performs better than single ARIMA model or SVM
model
Start-up: SVM Capital
• conduct global equity investing via a synergistic combination of machine insights from big data and
human insights and judgment.
• SVM Capital uses SVMs, and other AI techniques, in its investing process.
• The investment horizon is medium-term.
Raphael Rottge
• Education: B.S., Finance & Decision Sciences (Upenn), B.A., Psychology (Upenn), Mater in Computer
Science (Pontifícia Universidade Católica do Rio de Janeiro)
• Working Experience: 10+ years of worldwide financial markets experience in long-short equity and
M&A, Emerging markets entrepreneur