An asymptotic test for constancy of the variance under short-range dependence

We present a novel approach to test for heteroscedasticity of nonstationary time series that is based on Gini’s mean difference logarithmic local sample variances. In order analyse the large behaviour our statistic, we establish new limit theorems U-statistics dependent triangular arrays. derive asymptotic distribution statistic under null hypothesis constant variance and show consistent against class alternatives, including multiple structural breaks in variance. Our applicable even case processes, assuming locally stationary function. The performance its comparatively low computation are illustrated an extensive simulation study. As application, Google Trends data, monitoring relative search interest topic “global warming.”