Sieve bootstrap inference for linear time-varying coefficient models

Abstract

We propose a sieve bootstrap framework to conduct pointwise and simultaneous inference for time-varying coefficient regression models based on a local linear estimator. The asymptotic validity of the sieve bootstrap in the presence of autocorrelation is established. The bootstrap automatically produces a consistent estimate of nuisance parameters, both at the interior and boundary points. In addition, we develop a bootstrap-based test for parameter constancy and examine its asymptotic properties. An extensive simulation study demonstrates a good finite sample performance of our methods. The proposed methods are applied to assess the price development of CO2 certificates in the European Emissions Trading System. We find evidence of time variation in the relationship between allowance prices and their fundamental price drivers. The time variation might offer an explanation for previous contradicting findings using linear regression models with constant coefficients.