Prediction of actual symbol probability is crucial for statistical data compression that uses arithmetic coder. Krichevsky-Trofimov (KT) estimator has been a standard predictor and applied in CTW or FWCTW methods. However, KT-estimator performs poorly when non occurring symbols appear. To rectify this we proposed a zero-redundancy estimator, especially with a finite window(Rashid and Kawabata, ISIT2003) for non stationary source. In this paper, we analyze the zero-redundancy estimators in the case of Markovian source and give an asymptotic evaluation of the redundancy. We show that one of the estimators has the per symbol redundancy given by one half of the dimension of positive parameters divided by the window size when the window size is large.