Band Spectral Regression with Trending Data

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The thick market effect on local unemployment rate fluctuations (2006, unknown): “When the relationship is frequency-dependent, a detrending regression in the time domain can generate biased estimates, see Corbae et al. (2002). On the contrary, the band spectrum regression best captures the essence that the coefficients of trend variables are frequency-dependent and it leads to c”
Local Whittle estimation in nonstationary and unit root cases (2004, background): “[See also Corbae, Ouliaris and Phillips (2002), who give exact formulae for d.f.t.’s of a time trend whenα is a positive integer.]”
Frequency Dependence in Regression Model Coefficients: An Alternative Approach for Modeling Nonlinear Dynamic Relationships in Time Series (2008, result): “Also, in view of the criticism of linear de–trending in the context of spectral regression given by Corbae, Ouliaris and Phillips (2002) , it is notable that the results are not sensitive to how or even whether the within–window de–trending described at the end of Section 5 above is done.”