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Time series Forecasting using SVM

Kyoung-jae Kim

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- 1. Financial time series forecasting using support vector 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 ndimensional 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: 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. 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 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. 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

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