Abstract
The Hodrick–Prescott (HP) filter has been a popular method of trend extraction from economic time series. However, it is impractical without modification if some observations are not available. This paper improves the HP filter so that it can be applied in such situations. More precisely, this paper introduces two alternative generalized HP filters that are applicable for this purpose. We provide their properties and a way of specifying those smoothing parameters that are required for their application. In addition, we numerically examine their performance. Finally, based on our analysis, we recommend one of them for applied studies.
Highlights
The Hodrick–Prescott (HP) (1997) filter has been a popular method of trend extraction from economic time series such as real gross domestic product and has attracted a lot of attention among econometricians
We introduce two generalized HP filters, denoted by gHPn filter and gHPT filter, that are applicable for trend extraction of available observations
Even though the HP filter has been a popular method of trend extraction from economic time series, it is impractical without suitable modification if some observations are missing
Summary
The Hodrick–Prescott (HP) (1997) filter has been a popular method of trend extraction from economic time series such as real gross domestic product and has attracted a lot of attention among econometricians. Recent studies of the filter include de Jong and Sakarya (2016); Cornea-Madeira (2017); Hamilton (2018); Phillips and Jin (2020); Phillips and Shi (2020); Sakarya and de Jong (2020); Yamada (2012, 2015, 2018a, 2018b, 2020a, 2020b); Yamada and Du (2019), and Yamada and Jahra (2019). We introduce two generalized HP filters, denoted by gHPn filter and gHPT filter, that are applicable for trend extraction of available observations. We provide their properties and a way of specifying their smoothing parameters that are required for their application. The trend estimated by the Hodrick–Prescott (HP) filter with λ = 1600, denoted by HP filter , is superimposed onto Figure 1 Note that it is estimated from available observations, and missing observations.
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