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The spectral analysis of the Hodrick–Prescott filter

Sakarya, Neslihan and Jong, Robert M (2022) 'The spectral analysis of the Hodrick–Prescott filter.' Journal of Time Series Analysis, 43 (3). pp. 479-489. ISSN 0143-9782

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Abstract

The Hodrick–Prescott (HP) filter is a commonly used tool in macroeconomics to obtain the HP filter trend of a macroeconomic variable. In macroeconomics, the difference between the original series and this trend is called the ‘cyclical component’. In this article, we derive the autocovariance function and the spectrum of the cyclical component of a series that consists of a constant, a linear time trend, a unit root process, and a weakly stationary process. We show that the autocovariance function of the cyclical component of such a series depends on (i) the autocovariance of the innovations of the unit root process; (ii) the autocovariance of the weakly stationary process and; (iii) a component of the weights of the HP filter that is important in the middle of a large sample. The result for the spectrum of the cyclical component matches with earlier results in the literature that were obtained by using an approximate approach. Lastly, we derive the cross-covariance function and the cross-spectrum of the cyclical components of two cointegrated series.

Item Type: Article
Uncontrolled Keywords: Hodrick–Prescott filter; autocovariance function; spectrum; cross-covariance function; cross-spectrum; cointegration;
Divisions: Faculty of Social Sciences
Faculty of Social Sciences > Economics, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 13 Oct 2021 14:10
Last Modified: 14 Apr 2022 06:52
URI: http://repository.essex.ac.uk/id/eprint/31007

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