Prediction of Continuous Time Autoregressive Processes via the Reproducing Kernel Spaces

We study the statistical prediction of a continuous time stochastic process admitting a functional autoregressive representation. We construct an approximation of Parzen's optimal predictor in reproducing kernel spaces framework. This approach did not require an estimation of the operator of the autoregressive representation. This revised version was published online in August 2006 with corrections to the Cover Date.