Limit theorems for locally stationary processes

Kawka, Rafael

doi:10.1007/s00362-020-01204-1

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Hac Standard Errors In the Linear Regression Model1

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2022

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“…Define η t,T = x t,T u t,T and assume that {η t,T } 1≤t≤T ;T ∈N is locally stationary. By the central limit theorem for locally stationary processes (see Kawka, 2019, Theorem 2.1) it holds that…”

Section: Hac Standard Errors In the Linear Regression Modelmentioning

confidence: 99%

Convergence of spectral density estimators in the locally stationary framework

Kawka¹

2022

Econometrics and Statistics

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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, λ) standard spectral density estimators consistently estimate the time-averaged spectral density 1 0 f (u, λ) 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.

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Section: Hac Standard Errors In the Linear Regression Modelmentioning

confidence: 99%