  A general class of time-varying regression models is considered in this
paper. We estimate the regression coefficients by using local linear
M-estimation. For these estimators, weak Bahadur representations are obtained
and are used to construct simultaneous confidence bands. For practical
implementation, we propose a bootstrap based method to circumvent the slow
logarithmic convergence of the theoretical simultaneous bands. Our results
substantially generalize and unify the treatments for several time-varying
regression and auto-regression models. The performance for ARCH and GARCH
models is studied in simulations and a few real-life applications of our study
are presented through analysis of some popular financial datasets.
