论文标题
在高维度测试Martingale差异假设
Testing the martingale difference hypothesis in high dimension
论文作者
论文摘要
在本文中，我们考虑测试高维时间序列的Martingale差异假设。我们的测试建立在拟议矩阵值的非线性依赖度度量的不同滞后元素最大值的平方之和。为了进行推断，我们通过高斯近似值近似测试统计量的零分布，并提供了基于模拟的方法来产生临界值。还研究了替代方法下测试统计数据的渐近行为。我们的方法是非参数的，因为无效假设仅假设相关时间序列是在没有指定其条件力矩的任何参数形式的情况下进行的。作为高斯近似的优势，我们的测试对未知幅度的跨串行依赖性是可靠的。据我们所知，这是针对Martingale差异假设的第一个有效测试，该假设不仅允许大尺寸，还可以捕获非线性串行依赖性。通过模拟和实际数据分析说明了我们的测试的实际实用性。该测试以用户友好的R功能实现。
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at different lags. To conduct the inference, we approximate the null distribution of our test statistic by Gaussian approximation and provide a simulation-based approach to generate critical values. The asymptotic behavior of the test statistic under the alternative is also studied. Our approach is nonparametric as the null hypothesis only assumes the time series concerned is martingale difference without specifying any parametric forms of its conditional moments. As an advantage of Gaussian approximation, our test is robust to the cross-series dependence of unknown magnitude. To the best of our knowledge, this is the first valid test for the martingale difference hypothesis that not only allows for large dimension but also captures nonlinear serial dependence. The practical usefulness of our test is illustrated via simulation and a real data analysis. The test is implemented in a user-friendly R-function.
