论文标题
在短距离依赖性下方差恒定的渐近测试
An Asymptotic Test for Constancy of the Variance under Short-Range Dependence
论文作者
论文摘要
我们提出了一种基于Gini对数局部样本方差的平均差异的非平稳时间序列的异质性测试的新方法。为了分析测试统计量的大型样本行为，我们为依赖三角阵列的U统计数据建立了新的限制定理。我们在恒定方差的零假设下得出了测试统计量的渐近分布，并表明该测试与大量替代方案（包括方差中的多个结构断裂）保持一致。即使在非平稳过程的情况下，我们的测试也适用，假设存在局部固定的平均函数。在一项广泛的模拟研究中说明了测试的性能及其相对较低的计算时间。作为应用程序，我们分析了Google趋势数据，监视“全球变暖”主题的相对搜索兴趣。
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 Google Trends data, monitoring the relative search interest for the topic "global warming."
