Convolution Skew-$t$ Distributions

Xinxian Chen, Peter Reinhard Hansen and Chen Tong

Papers from arXiv.org

Abstract: We introduce the convolution skew-$t$ (CST) distribution, which combines independent standardized skew-$t$ subvectors through a general loading matrix to accommodate heterogeneous tails, directional asymmetry, and non-elliptical dependence. We establish identification and develop likelihood inference using analytical scores and a one-dimensional reduction of Fisher information. For the finite-variance model, we prove consistency and asymptotic normality of maximum likelihood and characterize the consequences of imposing false symmetry. A raw representation extends the family to all positive tail indices. Simulations assess finite-sample performance, and a realized-volatility application illustrates the empirical value of allowing tail thickness and asymmetry to vary across latent subvectors.

Date: 2026-10
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