Simultaneous inference for time-varying models

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