Differentiate Between White Noise And Martingale Different Sequence By Nonstationarity Measure

As the complexity of the system and our limitations of understanding and observational approaches.It difficult to understanding their microstructure accurately. For this point,the system can be regarded as a data generation process.We can study the evolution of the system through the output data of the system.In this paper, we studied some problems about the nonstationarity of data flow on the basis of the stability of frequency sequence and the concept of information structures by using related ideas of ergodic theory,coarse grain and information theory.First,we divised the phase of data flow by coarse grain and extracted information structure by judge the stability of the frequency sequence of subset in the phase space of data flow.Second,we made the supermum of shannon information entropy as entropy of data flow. An effective approximately algorithm is desibned for nonstationarity measure.We think the nonstationarity measure is smaller for a more stationary data flow.based on this,we can determine the stationary of different data flow by campare their nonstationarity measure.In application,we selected a number of classic white noise process and martingale difference sequences,including stationary and nonstationarity process. We can differentiate between white noise process and martingale difference sequences by calculating their nonstationarity measure. The numerical results shown that the nonstationarity measure is sound a good index to compare the level of nonstationarity among data flows.