Sieve bootstrap inference for time-varying coefficient models

We propose a sieve bootstrap framework to conduct pointwise and simultaneous inference for time-varying coefficient regression models based on a nonparametric local linear estimator. The asymptotic validity of the sieve bootstrap in the presence of autocorrelation is established. We find that it automatically produces a consistent estimation of nuisance parameters, both at the interior and boundary points. In addition, we develop a bootstrap test for parameter constancy and show that it is asymptotically correctly sized. An extensive simulation study supports our findings. The proposed methods are applied to assess the price development of CO2 certificates in the European Emissions Trading System (EU ETS). We find evidence of time variation in the relationship between allowance prices and their fundamental price drivers.