<p>We develop a functional-copula framework for analysing sectoral equity markets in a multivariate, tail-aware fashion. Daily log prices of twenty-one large-cap U.S. stocks, chosen to provide broad cross-sector coverage under the GICS classification over 2016–2024, are first smoothed into stock-specific curves using a B-spline basis, where both the number of basis functions and the smoothing parameter are selected automatically via a two-dimensional generalized cross-validation grid. From these curves, we extract a small number of functional principal components that summarise market-wide trends, sectoral rotations and higher-frequency adjustments, with five harmonics explaining 95.5% of the cross-sectional variation. The joint distribution of the resulting factor scores is then modelled using a regular vine (R-vine) copula, which allows for flexible nonlinear and asymmetric dependence beyond Gaussian correlation structures. Empirically, we document a strongly low-dimensional functional factor structure together with moderate but non-negligible non-elliptical dependence in the factor space, including tail-relevant linkages on selected pair-copula edges. A bootstrap goodness-of-fit check based on the vine log-likelihood does not reject the fitted specification, and robustness checks under a coarser smoothing basis confirm that the FPCA decomposition and vine fit remain stable. Overall, there appear to be relatively few sector-focused studies that combine a fully data-driven B-spline FPCA representation with a vine-copula dependence model in this way, and our results suggest that the proposed framework can serve as a transparent and reproducible tool for sector allocation, scenario design, stress testing and risk management.</p>

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Multidimensional analysis of sectoral equity dynamics: deconstructing market trends via functional data and vine copula integration

  • Çağlar Sözen

摘要

We develop a functional-copula framework for analysing sectoral equity markets in a multivariate, tail-aware fashion. Daily log prices of twenty-one large-cap U.S. stocks, chosen to provide broad cross-sector coverage under the GICS classification over 2016–2024, are first smoothed into stock-specific curves using a B-spline basis, where both the number of basis functions and the smoothing parameter are selected automatically via a two-dimensional generalized cross-validation grid. From these curves, we extract a small number of functional principal components that summarise market-wide trends, sectoral rotations and higher-frequency adjustments, with five harmonics explaining 95.5% of the cross-sectional variation. The joint distribution of the resulting factor scores is then modelled using a regular vine (R-vine) copula, which allows for flexible nonlinear and asymmetric dependence beyond Gaussian correlation structures. Empirically, we document a strongly low-dimensional functional factor structure together with moderate but non-negligible non-elliptical dependence in the factor space, including tail-relevant linkages on selected pair-copula edges. A bootstrap goodness-of-fit check based on the vine log-likelihood does not reject the fitted specification, and robustness checks under a coarser smoothing basis confirm that the FPCA decomposition and vine fit remain stable. Overall, there appear to be relatively few sector-focused studies that combine a fully data-driven B-spline FPCA representation with a vine-copula dependence model in this way, and our results suggest that the proposed framework can serve as a transparent and reproducible tool for sector allocation, scenario design, stress testing and risk management.