Testing for General Dynamical Stationarity with a Symbolic Data Compression Technique

We construct a statistic and null test for examining the stationarity of time-series of discrete symbols: whether two data streams appear to originate from the same underlying unknown dynamical system, and if any difference is statistically significant. Using principles and computational techniques from the theory of data compression, the method intelligently accounts for the substantial serial correlation and nonlinearity found in realistic dynamical data, problems which bedevil naive methods. Symbolic methods are computationally efficient and robust to noise. We demonstrate the method on a number of realistic experimental datasets.