Financial time series forecasting using supportvector machinesAuthor: Kyoung-jae Kim2003 Elsevier B.V.

OutlineIntroduction to SVMIntroduction to datasetsExperimental settingsAnalysis of experimental results

Linear separabilityLinear separabilityIn general, two groups are linearly separable inn-dimensional space if they can be separated by an (n1)-dimensionalhyperplane.

Support Vector MachinesMaximum-margin hyperplane

FormalizationTraining data

Hyperplane

Parallel bounding hyperplanes

ObjectiveMinimize (in w, b)||w||subject to (for any i=1, , n)

A 2-D caseIn 2-D:Training data:

xici11-1-1

Not linear separable No hyperplane can separate the two groups

Soft MarginChoose a hyperplane that splits the examples as cleanly as possibleStill maximizing the distance to the nearest cleanly split examplesIntroduce an error cost C

Higher dimensionsSeparation might be easier

Kernel TrickBuild maximal margin hyperplanes in high-dimenisonal feature space depends on inner product: more costUse a kernel function that lives in low dimensions, but behaves like an inner product in high dimensions

KernelsPolynomialK(p, q) = (pq + c)dRadial basis functionK(p, q) = exp(-||p-q||2)Gaussian radial basisK(p, q) = exp(-||p-q||2/22)

Tuning parametersError weightCKernel parameters2dc0

Underfitting & OverfittingUnderfitting

Overfitting

High generalization ability

DatasetsInput variables12 technical indicatorsTarget attributeKorea composite stock price index (KOSPI)2928 trading days80% for training, 20% for holdout

Settings (1/3) SVMkernelspolynomial kernelGaussian radial basis function2error cost C

Settings (2/3)BP-Networklayers3number of hidden nodes6, 12, 24learning epochs per training example50, 100, 200learning rate0.1momentum0.1input nodes12

Settings (3/3)Case-Based Reasoningk-NNk = 1, 2, 3, 4, 5distance evaluationEuclidean distance

Experimental resultsThe results of SVMs with various C where 2 is fixed at 25Too small Cunderfitting*Too large Coverfitting** F.E.H. Tay, L. Cao, Application of support vector machines in -nancial time series forecasting, Omega 29 (2001) 309317

Experimental resultsThe results of SVMs with various 2 where C is fixed at 78Small value of 2overfitting*Large value of 2underfitting** F.E.H. Tay, L. Cao, Application of support vector machines in -nancial time series forecasting, Omega 29 (2001) 309317

Experimental results and conclusionSVM outperformes BPN and CBRSVM minimizes structural riskSVM provides a promising alternative for financial time-series forecastingIssuesparameter tuning