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

Music City Center 

Expected shortfall is defined as the truncated mean of a random variable that falls below a specified quantile level. This statistic 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 in this manuscript. Existing estimation methods for such models typically rely on minimizing a nonlinear and nonconvex joint loss function, which is challenging to solve and often yields inefficient estimators. We employ a weighted two-step estimation approach to estimate the proposed models. Our proposed 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. 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.

Expected Shortfall

Time Series

Financial Risk Management

Neyman Orthogonality

Quantile Regression 

Business and Economic Statistics Section