关键词: 数据分析, 非平稳性度量, 模型选择, 稳定集合, Shannon信息熵

Abstract:

We study the nonstationarity measure for data streams by integration ideas from ergodic theory, coarse grain and information theory. We introduce nonstationarity measure for data streams. An effective approximation algorithm is designed for implementation. The nonstationarity measure is a real number between 0 and 1. The nonstationarity measure is smaller for a more stationary data stream. We apply the nonstationarity measure to model selection, and propose a criterion for model selection which requires least nonstationarity measure for residual sequence. Numerical experiments are performed to test our approximation algorithm and to validate the least nonstationarity measure as a criterion for model selection. The numerical results indicate that the nonstationarity measure is a sound index to compare the level of
nonstationarity among data streams. By comparing the nonstationarity measure, we can distinguish trend-stationary process and difference-stationary process effectively, and discern i.i.d. sequence, white noise sequence and martingale difference sequence.

Key words: Data analysis, Nonstationarity measure, Model selection, Stable set, Shannon entropy