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 then modify it by adapting a previously proposed double kernel estimator in order to provide greater accuracy for tail quantiles that are changing relatively quickly over time. We introduce double ker...