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Hodrick-Prescott filter for trend and cyclical components

`hpfilter(`

plots the data of the time series variables (columns) of `Y`

)`Y`

and their respective trend components computed by the Hodrick-Prescott Filter. The smoothing parameter is `1600`

, which is appropriate for quarterly periodicity[1]. `hpfilter`

plots all time series and their respective trend components on the same axes.

For high-frequency series, the Hodrick-Prescott filter can produce anomalous endpoint effects. In this case, do not extrapolate the series using the results of the filter.

[1] Hodrick, Robert J., and Edward C. Prescott. "Postwar U.S. Business Cycles: An Empirical Investigation." *Journal of Money, Credit and Banking* 29, no. 1 (February 1997): 1–16. https://doi.org/10.2307/2953682.