Symbolic aggregate approximation (SAX) is a typical and effective symbolic feature representation method. At present, there are many practical applications of the SAX method, but the analysis of its intrinsic properties, such as complexity, information loss, correlation and periodicity, is relatively rare. In this paper, we apply the permutation entropy to analyze the complexity and statistics characteristics of the relative intrinsic properties of the SAX method. Experiments on benchmark datasets and real clinical data show that the SAX method can significantly reduce the complexity of feature representation and alleviate the redundancy effect while preserving the inherent correlation measured by the autocorrelation function ACF. This work can provide support for the SAX method and its further application, and provide analytical and statistical tools for the design and evaluation of new symbolic representation methods.