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The paper re-investigates the efficiency of the East European emerging markets of the Czech Republic, Hungary, Poland and Russia analyzed by Rockinger and Urga (2000, 2001) based on the data from September, 1995 through December, 2004. We propose a first-order autoregressive (AR (1)) type time varying parameter model with a non-stochastic linear time trend including the random walk (RW) type model as a special case. The observed data rejects the RW type model for the AR (1) type one. The markets exhibit dynamic efficiency for all the four countries in the sense that the linear time trend approaches to zero over time. The empirical result for the Russian markets differs from that of Rockinger and Urga (2000). [ABSTRACT FROM AUTHOR]