An asymptotic test for constancy of the variance under short-range dependence
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Date
2020
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Abstract
We present a novel approach to test for heteroscedasticity of
a non-stationary time series that is based on Gini's mean difference of
logarithmic local sample variances. In order to analyse the large sample behaviour
of our test statistic, we establish new limit theorems for U-statistics
of dependent triangular arrays.We derive the asymptotic distribution of the
test statistic under the null hypothesis of a constant variance and show that
the test is consistent against a large class of alternatives, including multiple
structural breaks in the variance. Our test is applicable even in the case
of non-stationary processes, assuming a locally stationary mean function.
The performance of the test and its comparatively low computation time
are illustrated in an extensive simulation study. As an application, we analyse
data from civil engineering, monitoring crack widths in concrete bridge
surfaces.
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Keywords
change-point analysis, tests for heteroscedasticity, U-statistics of triangular arrays, short-range dependence