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 maximum-margin hyperplane

5. Formalization • Training data • Hyperplane • Parallel bounding hyperplanes

6. Objective • Minimize (in w, b) ||w|| • subject to (for any i=1, …, n)

7. A 2-D case • In 2-D: • Training data: -2x+2y+1=0 -2x+2y+1=1 -2x+2y+1=-1 w=<-2, 2> b=-1 margin=sqrt(2)/2

8. 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 d*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

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. Tuning parameters • Error weight • C • Kernel parameters • δ2 • 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

16. Settings (1/3) • SVM • kernels • polynomial kernel • Gaussian radial basis function • δ2 • error cost C

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. 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 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. 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. 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