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Title: Simultaneous inference for curve estimation in time-varying models Authors:  Stefan Richter - Heidelberg University (Germany)
Wei Biao Wu - University of Chicago (United States)
Sayar Karmakar - University of Florida (United States) [presenting]
Abstract: A general class of time-varying regression models which cover general linear models as well as time series models is considered. We estimate the regression coefficients by using local linear $M$-estimation. For these estimators, 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. The 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.