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dc.creatorPaige, Robert L.
dc.creatorTrindade, A. Alexandre (TTU)
dc.date.accessioned2022-05-28T15:50:20Z
dc.date.available2022-05-28T15:50:20Z
dc.date.issued2010
dc.identifier.citationPaige, R. L., & Trindade, A. A. (2010). The Hodrick-Prescott Filter: A special case of penalized spline smoothing. Electronic Journal of Statistics, 4, 856-874, 819. https://doi.org/10.1214/10-EJS570en_US
dc.identifier.urihttps://doi.org/10.1214/10-EJS570
dc.identifier.urihttps://hdl.handle.net/2346/89336
dc.description© 2010 The Institute of Mathematical Statistics and the Bernoulli Society. This work is licensed under a Creative Commons Attribution 4.0 International License.en_US
dc.description.abstractWe prove that the Hodrick-Prescott Filter (HPF), a commonly used method for smoothing econometric time series, is a special case of a linear penalized spline model with knots placed at all observed time points (except the first and last) and uncorrelated residuals. This equivalence then furnishes a rich variety of existing data-driven parameter estimation methods, particularly restricted maximum likelihood (REML) and generalized cross-validation (GCV). This has profound implications for users of HPF who have hitherto typically relied on subjective choice, rather than estimation, for the smoothing parameter. By viewing estimates as roots of an appropriate quadratic estimating equation, we also present a new approach for constructing confidence intervals for the smoothing parameter. The method is akin to a parametric bootstrap where Monte Carlo simulation is replaced by saddlepoint approximation, and provides a fast and accurate alternative to exact methods, when they exist, e.g. REML. More importantly, it is also the only computationally feasible method when no other methods, exact or otherwise, exist, e.g. GCV. The methodology is demonstrated on the Gross National Product (GNP) series originally analyzed by Hodrick and Prescott (1997). With proper attention paid to residual correlation structure, we show that REML-based estimation delivers an appropriate smooth for both the GNP series and its returns.en_US
dc.language.isoengen_US
dc.subjectEconometric Smoothingen_US
dc.subjectGross National Producten_US
dc.subjectParametric Bootstrap Confidence Intervalen_US
dc.subjectSaddlepoint Approximationen_US
dc.subjectSemiparametric Modelen_US
dc.titleThe Hodrick-Prescott Filter: A special case of penalized spline smoothingen_US
dc.typeArticleen_US


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