Simultaneous inference for time-varying models

TL;DR

This paper develops a unified framework for simultaneous inference in general time-varying regression models using local linear M-estimation, bootstrap methods, and applies it to financial data.

Contribution

It introduces a general approach for constructing simultaneous confidence bands in time-varying models, extending existing methods and improving practical implementation.

Findings

Bootstrap method effectively circumvents slow convergence of confidence bands.

Method successfully applied to ARCH and GARCH models in simulations.

Real-world financial datasets demonstrate the approach's practical utility.

Abstract

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.