REGIME VARIANCE TESTING - A QUANTILE APPROACH

In this paper, we examine time series that exhibit behavior related to two or more regimes with different statistical properties. The motivation of our study are two real data sets from plasma physics with an observable two-regimes structure. In this paper, we develop a procedure to estimate the critical point of the division in a structural change in a time series. Moreover, we propose three tests to recognize such specific behavior. The presented methodology is based on the empirical second moment and its main advantage is the assumption of a lack of distribution. Moreover, the examined statistical properties are expressed in the language of empirical quantiles of the squared data, therefore, the methodology is an extension of the approach known from the literature. Theoretical results are confirmed by simulations and analysis of real data of turbulent laboratory plasma.