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We find upper bounds for the probability of underestimation andoverestimation errors in penalized likelihood context tree estimation. Thebounds are explicit and applies to processes of not necessarily finite memory.We allow for general penalizing terms and we give conditions over the maximaldepth of the estimated trees in order to get strongly consistent estimates.This generalizes previous results obtained in the case of estimation of theorder of a Markov chain.

Some upper bounds for the rate of convergence of penalized likelihood context tree estimators