There is little evidence on the efficiency of the early stage of the capital market in transition countries, although market structure developments and the learning process could define the framework for efficient markets. The article tries to find out whether financial markets are efficient in the three Baltic States and if not, whether there are any signs of evolving to the efficient capital market. To answer these questions the analysis combines the methodology for testing the efficiency of capital market using the variance ratio robust to heteroscedasticity with the state-space representation, which enables us to use an efficient filtering technique - the Kalman filter - to get time varying autocorrelations. The official Estonian, Latvian, and Lithuanian stock exchange market indices TALSE, DJRSE, and LITIN comprising the most liquid parts of the stock market in a respective country are analysed. The main conclusion to be drawn from the analysis is that financial markets in the Baltic States are, with some turbulence, approaching weak form of efficiency.
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