Hodrick-Prescott Filter

The Hodrick-Prescott Filter is a smoothing method that is widely used among macroeconomists to obtain a smooth estimate of the long-term trend component of a series. The method was first used in a working paper (circulated in the early 1980’s and published in 1997) by Hodrick and Prescott to analyze postwar U.S. business cycles.

Technically, the Hodrick-Prescott (HP) filter is a two-sided linear filter that computes the smoothed series of by minimizing the variance of around , subject to a penalty that constrains the second difference of . That is, the HP filter chooses to minimize:

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The penalty parameter controls the smoothness of the series . The larger the , the smoother the . As , approaches a linear trend.

To smooth the series using the Hodrick-Prescott filter, choose Proc/Hodrick-Prescott Filter…:

First, provide a name for the smoothed series. EViews will suggest a name, but you can always enter a name of your choosing. Next, specify an integer value for the smoothing parameter, . You may specify the parameter using the frequency power rule of Ravn and Uhlig (2002) (the number of periods per year divided by 4, raised to a power, and multiplied by 1600), or you may specify directly. The default is to use a power rule of 2, yielding the original Hodrick and Prescott values for :

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Ravn and Uhlig recommend using a power value of 4. EViews will round any non-integer values that you enter. When you click OK, EViews displays a graph of the filtered series together with the original series. Note that only data in the current workfile sample are filtered. Data for the smoothed series outside the current sample are filled with NAs.