Convergence of spectral density estimators in the locally stationary framework

Locally stationary processes are characterised by spectral densities that are functions of rescaled time. We study the asymptotic properties of spectral density estimators in the locally stationary framework. In particular, we show that for a locally stationary process with time-varying spectral density function f(u; ) standard spectral density estimators consistently estimate the time-averaged spectral density R 1 0 f(u; ) du. This result is complemented by some illustrative examples and applications including HAC-inference in the multiple linear regression model and a simple visual tool for the detection of unconditional heteroskedasticity