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

Thomas M. Menino Convention & Exhibition Center 

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 employ a weighted two-step regression approach to estimate the proposed model and focus on estimating and inferring the expected shortfall model parameters. By constructing weighting functions that match the conditional variance of the regression residuals, our proposed expected shortfall estimator has greater efficiency compared to those obtained by existing methods, both theoretically and numerically, for a general class of location-scale family time series. We further develop a Portmanteau test for model diagnostics with theoretical guarantees. 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.

Time Series

Financial Risk Management

Neyman Orthogonality

Quantile Regression