Financial time series forecasting using support vector machines

1
Financial time series forecasting using
supportvector machines

• Author Kyoung-jae Kim
• 2003 Elsevier B.V.

2
Outline

• Introduction to SVM
• Introduction to datasets
• Experimental settings
• Analysis of experimental results

3
Linear separability

• Linear separability
• In general, two groups are linearly separable
  in n-dimensional space if they can be separated
  by an (n - 1)-dimensional hyperplane.

4
Support Vector Machines

• Maximum-margin hyperplane

5
Formalization

• Training data
• Hyperplane
• Parallel bounding hyperplanes

6
Objective

• Minimize (in w, b)
• w
• subject to (for any i1, , n)

7
A 2-D case

• In 2-D
• Training data

xi ci
lt1, 1gt 1
lt2, 2gt 1
lt2, 1gt -1
lt3, 2gt -1
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Not linear separable

• No hyperplane can separate the two groups

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

10
Higher dimensions

• Separation might be easier

11
Kernel Trick

• Build maximal margin hyperplanes in
  high-dimenisonal 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

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Kernels

• Polynomial
• K(p, q) (pq c)d
• Radial basis function
• K(p, q) exp(-?p-q2)
• Gaussian radial basis
• K(p, q) exp(-p-q2/2d2)

13
Tuning parameters

• Error weight
• C
• Kernel parameters
• d2
• d
• c0

14
Underfitting Overfitting

• Underfitting
• Overfitting
• High generalization ability

15
Datasets

• Input variables
• 12 technical indicators
• Target attribute
• Korea composite stock price index (KOSPI)
• 2928 trading days
• 80 for training, 20 for holdout

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Settings (1/3)

• SVM
• kernels
• polynomial kernel
• Gaussian radial basis function
• d2
• error cost C

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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

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Settings (3/3)

• Case-Based Reasoning
• k-NN
• k 1, 2, 3, 4, 5
• distance evaluation
• Euclidean distance

19
Experimental results

• The results of SVMs with various C where d2 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) 309317
20
Experimental results

• The results of SVMs with various d2 where C is
  fixed at 78
• Small value of d2
• overfitting
• Large value of d2
• underfitting

F.E.H. Tay, L. Cao, Application of support
vector machines in -nancial time series
forecasting, Omega 29 (2001) 309317
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