Ratio Test for Time-Varying Variance of Mean Change Point Based on Big Data Analysis

There are more and more applications involve the big data analytics. The research method of big data is particularly important in the study of time-varying volatilities. In the article, we analysis the tests for a constant mean possibly subjected to change under strong mixing dependence based on big data method. The change point methods provided here rely on ratio type test statistics based on the functional of the partial sums of residuals. The main advantage of proposed approach is that the model allows strong mixing and time-varying variance in error terms. Based on the fundamental results suggested by Cavaliere (2004, Econometric Reviews, 23, 259− 292), the limiting distribution under the original hypothesis is derived and the consistency under the alternatives is also proved.