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The concept of context tree, usually defined for finite memory processes, is extended to arbitrary stationary ergodic processes (with finite alphabet). These context trees are not necessarily complete, and may be of infinite depth. The familiar BIC and MDL principles are shown to provide strongly consistent estimators of the context tree, via optimization of a criterion for hypothetical context trees of finite depth, allowed to grow with the sample size asdoi:10.1109/isit.2005.1523438 dblp:conf/isit/CsiszarT05 fatcat:ipphfazck5hjhje3tyoel2we3y