Toward Harmless Detrending

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This paper investigates effects of the Christiano-Fitzgerald (CF) detrending procedure, following Chan, Hayya, and Ord (1977) and Nelson and Kang (1981). The main findings are as follows. First, inclusion of an intercept term into detrending models creates artifactual cyclical components in the spectral density function (SDF) and introduces nonlinearity in the autocorrelation function (ACF) when the true data generating process follows the random walk. Second, the Christiano-Fitzgerald (CF)-type procedure with no intercept does not create artifactual cyclical components over the frequency range corresponding to the periods of cycles observable in sample. Finally, when the CF procedure is implemented with the mean-corrected time trend, the ACF of the transformed data does not show artifactual autocorrelations, and produces a good approximation to that of the true process. These findings lead to the conclusion that the CF procedure is harmless in the linear time trend removal in that it would create less distortion in SDF and ACF of the transformed data.

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