Sayar Karmakar : Simultaneous confidence bands in time-varying coefficient models

Posted by Yichao Wu , part of the Statistics and Data Science Seminar.

At

Oct. 25, 2017, 4 p.m.

In

SEO 636

Abstract

The term "time-varying(tv) coefficient model" refers to the framework of time series and regression models where the unknown coefficients vary across time. Deviation from the constancy of parameters is more natural due to the effect of several external factors/events or sometimes simply for a very long time-horizon. For the past two decades, tv regression models received considerable attentions however not much was done for  conditional heteroscedastic(CH) models until very recently.   The purpose of this talk is to introduce an unanimous framework to combine the treatments for tv linear regression, tv generalized regression and tv time-series models. Local linear M-estimation is used to estimate the unknown curves. We obtain a Bahadur representation of these estimated curves and use it to find the simultaneous confidence bands. To circumvent the logarithmic convergence rate of the theoretical bands, a Bootstrap method is proposed using an optimal Gaussian approximation. Some simulations for  tvARCH and tvGARCH models and analysis of some stock market datasets are presented. This is a joint work with Stefan Richter and Wei Biao Wu.