We propose exponentially weighted quantile regression (EWQR) for estimating time-varying quantiles. The EWQR cost function can be used as the basis for estimating the time-varying expected shortfall associated with the EWQR quantile forecast. We express EWQR in a kernel estimation framework, and...

Expectile models are derived using asymmetric least squares. A simple formula has been presented that relates the expectile to the expectation of exceedances beyond the expectile. We use this as the basis for estimating the expected shortfall. It has been proposed that the θ quantile be...