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Old 01-23-2014, 03:36 AM
rakhlin rakhlin is offline
Join Date: Jun 2012
Posts: 24
Default Re: VC dimension of time series models

Thank you very much, Professor.

I have overlooked this apparent fact that number of centers in RBF model equals to estimated parameters, weights, and hence VC-dimension.

For the sake of brevity I haven't explained what the models forecast. It does not affect you conclusion but it's an interesting part on its own. Forecast isn't binary, they forecast 2 real valued outputs: return and variance of return. For discrete state model these 2 values are just a constant average of similar states (2^k pairs). Absolute ratio of the 2 values considered as a proxy of predictability, the more the better, and affects size of investment. Eventually, they forecast binary direction and real valued investment size. On the other side, from a trader's viewpoint, decomposition of forecast into return and variance is concrete and mature approach. It is rare among works on financial forecasting I saw. I have a gut feeling that state-dependent or regime-dependent models is the right approach in financial forecasting (unlike many others). The article is very solid and fresh despite it was written 14 years ago. Klaus Pawelzik is co-author of Vapnik in "Predicting time series with support vector machnes" published in 1997 and has many interesting works in various fields.

Dear Professor, in this model I was going to substitute RBF network with support vector regression. But I remember you noticed ones that support vector regression isn't that good as SVM for classification is. Is it worth of trying? Stay with RBF?
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