Shiyao Huang, Xiaojun Song
arXiv 7 Oct 2026 · Econometrics
arXiv:2610.09351 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Lu, Xiaohui and Zhou, Yahong (2025) An Adaptive Kernel-Based Structural Change Test for Copulas | 1.000 | 14 | 5 | 100% |
| 2 | Chen, Xiaohong and Fan, Yanqin (2006) Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification | 1.000 | 13 | 5 | 100% |
| 3 | Nasri, Bouchra R and Rémillard, Bruno N and Bahraoui, Tarik (2022) Change-point problems for multivariate time series using pseudo-observations | 1.000 | 6 | 4 | 100% |
| 4 | Chan, N. and Chen, J. and Chen, X. and Fan, Y. and Peng, L (2009) Statistical inference for multivariate residual copula of GARCH models | 0.874 | 6 | 2 | 100% |
| 5 | Inglot, Tadeusz and Kallenberg, Wilbert CM and Ledwina, Teresa (1997) Data driven smooth tests for composite hypotheses | 0.811 | 4 | 2 | 100% |
| 6 | Janic-Wró, Alicja and Ledwina, Teresa (2000) Data driven rank test for two-sample problem | 0.811 | 4 | 2 | 100% |
| 7 | Kallenberg, Wilbert CM and Ledwina, Teresa (1997) Data-driven smooth tests when the hypothesis is composite | 0.811 | 4 | 2 | 100% |
| 8 | Kallenberg, Wilbert CM and Ledwina, Teresa (1999) Data-driven rank tests for independence | 0.811 | 4 | 2 | 100% |
| 9 | Ledwina, Teresa (1994) Data-driven version of Neyman's smooth test of fit | 0.811 | 4 | 2 | 100% |
| 10 | Kallenberg, Willibrordes Cornelis Maria and Ledwina, Teresa (1995) On data driven Neyman's tests | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 43 scored citations.