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We propose a robust recurrent kernel online learning (RRKOL) algorithm which allows the exploitation of the kernel trick in an online fashion. The novel RRKOL algorithm achieves guaranteed weight convergence with regularized risk management through the recurrent hyper-parameters for a superior generalization performance. To select useful data to be learned and remove redundant ones, a sparcification procedure is developed based on the stability analysis of the system. Two time-series prediction examples are presented.