I propose a novel way to generate bootstrapped (in-sample) confidence intervals for mis-specified observation-driven volatility models using a moving-window resampler. The new approach accounts for various sources of uncertainty, including parameter and filtering uncertainties. In particular, this method produces confidence bands around the time-varying volatility estimate with an GARCH filter. Average coverage achieved by the confidence bands tends to be close to the nominal level in finite samples and converges to the nominal level as the sampling frequency is increased. The procedure can also be employed as a smoother which reduces average root mean square error of point estimates at any frequency. Finite sample and convergence properties of this method are investigated in a range of simulation experiments. I further illustrate the usefulness of the method using S&P 500 returns. The proposed procedure is easily implementable and does not increase computational burden significantly. This novel methodology can be applied to many other observation-driven time-series models.