Financial time series forecasting
using support
vector machines
Author: Kyoung-jae Kim
2003 Elsevier B.V.
Outline
•
•
•
•

Introduction to SVM
Introduction to datasets
Experimental settings
Analysis of experimental results
Linear separability
• Linear separability
– In general, two groups are linearly separable in ndimensional space if they ca...
Support Vector Machines
• Maximum-margin hyperplane
maximum-margin hyperplane
Formalization
• Training data
• Hyperplane
• Parallel bounding hyperplanes
Objective
• Minimize (in w, b)
||w||

• subject to (for any i=1, …, n)
A 2-D case
• In 2-D:
– Training data:
xi

ci

<1, 1> 1
<2, 2> 1
<2, 1> -1
<3, 2> -1

-2x+2y+1=1

-2x+2y+1=0
-2x+2y+1=-1

w...
Not linear separable
• No hyperplane can separate the two groups
Soft Margin
• Choose a hyperplane that splits the examples
as cleanly as possible
• Still maximizing the distance to the n...
Higher dimensions
• Separation might be easier
Kernel Trick
• Build maximal margin hyperplanes in highdimenisonal feature space depends on inner
product: more cost
• Use...
Kernels
• Polynomial
– K(p, q) = (p•q + c)d

• Radial basis function
– K(p, q) = exp(-γ||p-q||2)

• Gaussian radial basis
...
Tuning parameters
• Error weight
–C

• Kernel parameters
– δ2
–d
– c0
Underfitting & Overfitting
• Underfitting
• Overfitting
• High generalization ability
Datasets
• Input variables
– 12 technical indicators

• Target attribute
– Korea composite stock price index (KOSPI)

• 29...
Settings (1/3)
• SVM
– kernels
• polynomial kernel
• Gaussian radial basis function
– δ2

– error cost C
Settings (2/3)
• BP-Network
– layers
• 3

– number of hidden nodes
• 6, 12, 24

– learning epochs per training example
• 5...
Settings (3/3)
• Case-Based Reasoning
– k-NN
• k = 1, 2, 3, 4, 5

– distance evaluation
• Euclidean distance
Experimental results
• The results of SVMs with various C where δ2 is fixed
at 25
• Too small C
• underfitting*

• Too lar...
Experimental results
• The results of SVMs with various δ2 where C is fixed
at 78
• Small value of δ2
• overfitting*

• La...
Experimental results and conclusion
• SVM outperformes BPN and CBR
• SVM minimizes structural risk
• SVM provides a promis...
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Time series Forecasting using svm

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Time series Forecasting using SVM

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Time series Forecasting using svm

  1. 1. Financial time series forecasting using support vector machines Author: Kyoung-jae Kim 2003 Elsevier B.V.
  2. 2. Outline • • • • Introduction to SVM Introduction to datasets Experimental settings Analysis of experimental results
  3. 3. Linear separability • Linear separability – In general, two groups are linearly separable in ndimensional space if they can be separated by an (n − 1)-dimensional hyperplane.
  4. 4. Support Vector Machines • Maximum-margin hyperplane maximum-margin hyperplane
  5. 5. Formalization • Training data • Hyperplane • Parallel bounding hyperplanes
  6. 6. Objective • Minimize (in w, b) ||w|| • subject to (for any i=1, …, n)
  7. 7. A 2-D case • In 2-D: – Training data: xi ci <1, 1> 1 <2, 2> 1 <2, 1> -1 <3, 2> -1 -2x+2y+1=1 -2x+2y+1=0 -2x+2y+1=-1 w=<-2, 2> b=-1 margin=sqrt(2)/2
  8. 8. Not linear separable • No hyperplane can separate the two groups
  9. 9. Soft Margin • Choose a hyperplane that splits the examples as cleanly as possible • Still maximizing the distance to the nearest cleanly split examples • Introduce an error cost C d*C
  10. 10. Higher dimensions • Separation might be easier
  11. 11. Kernel Trick • Build maximal margin hyperplanes in highdimenisonal feature space depends on inner product: more cost • Use a kernel function that lives in low dimensions, but behaves like an inner product in high dimensions
  12. 12. Kernels • Polynomial – K(p, q) = (p•q + c)d • Radial basis function – K(p, q) = exp(-γ||p-q||2) • Gaussian radial basis – K(p, q) = exp(-||p-q||2/2δ2)
  13. 13. Tuning parameters • Error weight –C • Kernel parameters – δ2 –d – c0
  14. 14. Underfitting & Overfitting • Underfitting • Overfitting • High generalization ability
  15. 15. Datasets • Input variables – 12 technical indicators • Target attribute – Korea composite stock price index (KOSPI) • 2928 trading days – 80% for training, 20% for holdout
  16. 16. Settings (1/3) • SVM – kernels • polynomial kernel • Gaussian radial basis function – δ2 – error cost C
  17. 17. Settings (2/3) • BP-Network – layers • 3 – number of hidden nodes • 6, 12, 24 – learning epochs per training example • 50, 100, 200 – learning rate • 0.1 – momentum • 0.1 – input nodes • 12
  18. 18. Settings (3/3) • Case-Based Reasoning – k-NN • k = 1, 2, 3, 4, 5 – distance evaluation • Euclidean distance
  19. 19. Experimental results • The results of SVMs with various C where δ2 is fixed at 25 • Too small C • underfitting* • Too large C • overfitting* * F.E.H. Tay, L. Cao, Application of support vector machines in -nancial time series forecasting, Omega 29 (2001) 309–317
  20. 20. Experimental results • The results of SVMs with various δ2 where C is fixed at 78 • Small value of δ2 • overfitting* • Large value of δ2 • underfitting* * F.E.H. Tay, L. Cao, Application of support vector machines in -nancial time series forecasting, Omega 29 (2001) 309–317
  21. 21. Experimental results and conclusion • SVM outperformes BPN and CBR • SVM minimizes structural risk • SVM provides a promising alternative for financial time-series forecasting • Issues – parameter tuning

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