发表机构
Peking University（北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于广义傅里叶系数的平滑检验方法，用于检测多元动态模型创新Copula的结构变化，具有oracle性质、无需bootstrap或带宽选择，并在稀疏备择下功效显著。
AI 中文摘要
本文针对多元动态模型的创新Copula结构变化，提出了新颖的平滑检验方法。我们通过一组广义傅里叶系数来刻画Copula非恒定性的偏离，并检验其联合显著性。在原假设下，动态参数和未知边际分布的估计对所提出的统计量没有一阶估计效应。因此，基于估计残差的可行检验与基于未观测创新的不可行检验渐近等价，从而具有理想的oracle性质。我们提出的检验统计量渐近服从χ²分布，并且对以参数速率趋近原假设的局部备择假设具有非平凡功效。为了增强方法的实用性，我们进一步开发了一种数据驱动程序，自动选择基展开的截断阶数。与基于经验Copula过程或核平滑的现有方法不同，我们的检验既不需要计算密集的bootstrap程序，也不需要带宽选择。大量模拟实验表明，我们提出的检验具有令人满意的经验水平和功效。特别是，数据驱动检验在稀疏备择假设下能带来显著的功效提升，同时在密集备择假设下保持竞争力。对汇率和股票收益的应用进一步说明了所提出方法的实际有用性。
英文摘要
This paper develops novel smooth tests for structural changes in the innovation copula of multivariate dynamic models. We characterize deviations from copula constancy through a collection of generalized Fourier coefficients and test their joint significance. Under the null hypothesis, estimation of the dynamic parameters and the unknown marginals has no first-order estimation effect on the proposed statistics. Consequently, the feasible tests based on estimated residuals are asymptotically equivalent to their infeasible counterparts based on the unobserved innovations, yielding a desirable oracle property. Our proposed tests are asymptotically $χ^2$-distributed and possess nontrivial power against local alternatives that approach the null at the parametric rate. To enhance the practicability of our methods, we further develop a data-driven procedure that automatically selects the truncation orders of the basis expansions. Unlike existing methods based on empirical copula processes or kernel smoothing, our tests require neither computationally intensive bootstrap procedures nor bandwidth selection. Extensive simulations demonstrate the satisfactory empirical size and power of our proposed tests. In particular, the data-driven test delivers substantial power gains under sparse alternatives, while remaining competitive under dense alternatives. Applications to exchange rates and stock returns further illustrate the practical usefulness of the proposed methods.
