In a post on my Blog in December 2011 I discussed how the Hodrick-Prescott filter can be viewed as the solution to a regression problem, and how this then enables one to construct confidence bands for the extracted trend component.

Here are the Eviews and gretl files that implement this idea. The gretl files are courtesy of Riccardo ("Jack") Luccetti:

EViews Workfile.

EViews program file.

gretl data file.

gretl script file.

References:

Danthine, J-P. and M. Girardin, 1989. Business cycles in Switzerland. European Economic Review, 33, 31-50.
Henderson, R., 1924. A new method of graduation. Transactions of the Actuarial Society of America, 25, 29-40.
Hodrick, R. J. and E. C. Prescott, 1980. Postwar U.S. business cycles: An empirical investigation. Discussion Paper  No. 451, Department of Economics, Carnegie Mellon University.
Hodrick, R. J. and E. C. Prescott, 1997. Postwar U.S. business cycles: An empirical investigation. Journal of Money, Credit, and Banking, 29, 1-16.
Leser, C. E. V., 1961. A simple method of trend construction. Journal of the Royal Statistical Society, B,  23, 91-107.
Ley, E., 2006. The Hodrick-Prescott filter. Knowledge Brief for Bank Staff, The World Bank, Washington D.C.
Polasek, W, 2011. The Hodrick-Prescott (HP) filter as a Bayesian regression model. WP 11-46, The Rimini Centre for Economic Analysis, Rimini, Italy.
Ravn, M. O. and H. Uhlig (2002). On adjusting the Hodrick-Prescott Filter for the Frequency of Observations. Review of Economics and Statistics, 84, 371-376.
Schlicht, E., 2005. Estimating the smoothing parameter in the so-called Hodrick-Prescott filter. Journal of the Japan Statistical Society, 35, 99-119.
Whittaker, E. T. (1922). On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41, 63-75.

Last Update: 24 February, 2021