Abstract: The non-stationarity of time series is closely related to its application in many fields. How to measure the non-stationarity of time series is an important research topic. A complete non-stationarity measurement framework has been constructed, in which the criterion of stable set is the core. In this paper, based on the law of iterated logarithm of independent identically distributed random variables, a new criterion of stable set is proposed. Compared with the existing criterion, the convergence criterion is more strict and requires fewer parameters when the level of significance is the same. This method improves the resolution of non-stationary measurement when NS is small. For the parameter calibration of deterministic signals, the new method can get more accurate results.

Key words: Non-stationary measure, Stable set, Law of the iterated logarithm