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用于 VaR 的 VAR：以多元回归分位数衡量尾部依赖AI 解读

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market equity returns data to analyze spillovers in the…

We explore the extension of James–Stein–type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator toward a fixed point, we shrink it toward a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James–Stein–type estimators shrunk toward a data-dependent point and prove that they have smaller asymptotic risk than the base estimator.…