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arXiv · 2610.25730

Estimation and Inference for the Joint Autoregressive Quantile-Expected Shortfall Model

Peiyao Cai·Kean Ming Tan·Xuming He
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Abstract

Expected shortfall is defined as the truncated mean of a random variable that falls below a specified quantile level and is widely recognized as an important risk measure. Motivated by the empirical observation of clustering patterns in financial risks, we consider a joint autoregressive model for both conditional quantile and expected shortfall. Existing estimation methods for such models typically rely on minimizing a nonlinear and nonconvex joint loss function, which is challenging to solve. We introduce a two-step regression framework to estimate the model parameters with theoretical guarantees. We further develop a Portmanteau test for model diagnostics and prove its asymptotic validity for Type I error control. Our empirical results on stock market data indicate that the proposed models effectively capture the clustering patterns and leverage effects on the conditional expected shortfall.

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Peiyao Cai, Kean Ming Tan, Xuming He. 2026-10-19. Estimation and Inference for the Joint Autoregressive Quantile-Expected Shortfall Model. https://arxiv.org/abs/2610.25730

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