We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are applied to the S&P 500 Index data.
"Confidence bands in nonparametric time series regression." Ann. Statist. 36 (4) 1854 - 1878, August 2008. https://doi.org/10.1214/07-AOS533