Convergence of spectral density estimators in the locally stationary framework
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Date
2019
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Abstract
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.