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I want to know how to use SVM to do time series prediction? what the differences of input vecvtor X of our model between time-series prediction and standard kernelized regression problem?

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The fundamental difference in case of time-series prediction against general regression problem (not only for SVM) is the dependence of response on more than one cases.

So, for example if the input vector with N cases is X1...XN, then for predicting some case number n, all the input-response data from X1 through Xn-1 can be used (and are supposed to effect its outcome).

Generally, a fixed number of cases immediately preceding the case to be predicted are used. One way to do time-series prediction with SVM is to transform your input variable X to include features derived from the desired number of preceding cases.

Here is a code example by Quantum Financer.

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