This article introduces a model, based on the Kalman-filter framework, that allows for time-varying parameters, latent factors, and a general generalized autoregressive conditional heteroscedasticity (GARCH) structure for the residuals. With this extension of the Bekaert and Harvey model, it is possible to test if an emerging stock market becomes more efficient over time and more integrated with other already established markets in situations in which no macroeconomic conditioning variables are available. We apply this model to the Czech, Polish, Hungarian, and Russian stock markets. We use data at daily frequency running from April 7, 1994. to July 10, 1997. A latent factor captures macroeconomic expectations. Concerning predictability, measured with time-varying autocorrelations, Hungary reached efficiency before 1994. Russia shows signs of ongoing convergence toward efficiency. For Poland and the Czech Republic, we find no improvements. With regard to market integration, there is evidence that the importance of Germany has changed over time for all markets. Shocks in the United Kingdom are positively related to the Czech and Polish markets but not to the Russian or the Hungarian markets. Shocks in the United States have no impact on these markets with the exception of Russia. A strong negative correlation between Russia and the United States and Germany tends to disappear over the time span studied. We also show that these markets exhibit significant asymmetric GARCH effects where bad news generates greater volatility. In Hungary, good news, instead, generates greater volatility, which leads us to formulate a liquidity hypothesis.