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This paper proposes a multi-step prediction model for time series prediction, i.e. Meta-cognitive Recurrent Kernel Online Sequential Extreme Learning Machine with Drift Detector Mechanism (Meta-RKOS-ELM ALD). Recurrent multi-step algorithm is applied to release the limitation in the number of prediction steps, and Drift Detector Mechanism (DDM) is used to overcome the problem of concept drift in the prediction model. The new meta-cognitive strategy decides the way of the incoming data during training, which decreases the training computation of prediction model and solves the parameter dependency. In our evaluation, we use a total of six artificial data sets and three real-world data sets (Standard & Poor's 500 Index, Shanghai Stock Exchange Composite Index, and Ozone Concentration in Toronto) to prove the ability of kernel filters, the detecting ability of concept drift detector, and situation of applying meta-cognitive strategy in our proposed model. Experiments results indicate that the Meta-KOS-ELM ALD with DDM has better forecasting ability in various predicting periods with the shortest learning time, as compared with other algorithms. [ABSTRACT FROM AUTHOR]