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？
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.