The term "time-varying (tv) coefficient models" refers to the collection of statistical models where the unknown coefficients/parameters vary across time. As an introduction, we will highlight the vast applicability of simultaneous inference for these parametric functions. The estimation and the construction of simultaneous confidence band (SCB) will be briefly discussed.
In the second part, we explore time-varying theme for complicated models such as ARCH, GARCH, ARMA-GARCH etc. We solve this problem in its most generality by introducing a framework that accounts for several time-varying regression and auto-regression models simultaneously. Such a general treatment calls for a local linear M-estimation of the coefficients and a Bahadur representation to construct the SCB. Bootstrap and sharp Gaussian approximation are used to circumvent logarithmic convergence of theoretical bands. I conclude my talk showing some simulations (time-permitting) and analysis for stock market and currency exchange datasets.