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A simple randomized algorithm for sequential prediction of ergodic time series

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3 Author(s)
Gyorfi, L. ; Dept. of Econ., Tech. Univ. Budapest, Hungary ; Lugosi, G. ; Morvai, G.

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from previous developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor. The desirable finite-sample properties of the predictor are illustrated by its performance for Markov processes. In such cases the predictor exhibits near-optimal behavior even without knowing the order of the Markov process. Prediction with side information is also considered

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Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 7 )