Abstract: Symbolic aggregate approximation(SAX) is a standard representation for time series data mining. However, very little work has been done about the intrinsic properties of this method. We proposed a statistical measurement, namely information embedding cost(IEC), to analyze the statistical behaviors of the symbolic dynamics. With IEC, we further build the Markov transition matrix from the SAX representation to visualize the time series as complex networks. The experiments on the benchmark datasets demonstrate that SAX can efficiently embed the time series with reduced complexity while preserve the core information. The IEC score provides a priori to determine if SAX is adequate for specific dataset, which can be generalized to evaluate other symbolic representations. We applied visualization approach together with IEC score to visu-ally understand, explore classification tasks and the intrinsic properties of SAX. A framework was provided to analyze, evaluate and further improve the symbolic dynamics for knowledge discovery in time series.