Filtering Time Series with Penalized Splines

Kauermann, Göran; Krivobokova, Tatyana; Semmler, Willi

doi:10.2202/1558-3708.1789

Cited by 12 publications

(9 citation statements)

References 34 publications

(15 reference statements)

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“…Eilers (2003) uses leave-one-out cross-validation to select this parameter. Kauermann, Krivobokova and Semmler (2011) work in the other direction, replacing the H-P filter with a penalized spline smoother.…”

Section: Source: Authors' Ownmentioning

confidence: 99%

L- and V-curves for optimal smoothing

Frasso

Eilers²

2014

Statistical Modelling

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The L-curve is a tool for the selection of the regularization parameter in ill-posed inverse problems. It is a parametric plot of the size of the residuals vs that of the penalty. The corner of the L indicates the right amount of regularization. In the context of smoothing the L-curve is easy to compute and works surprisingly well, even for data with correlated noise. We present the theoretical background and applications to real data together with an alternative criterion for finding the corner automatically. We introduce as simplification, the V-curve, which replaces finding the corner of the L-curve by locating a minimum.

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Section: Source: Authors' Ownmentioning

confidence: 99%

L- and V-curves for optimal smoothing

Frasso

Eilers²

2014

Statistical Modelling

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“…It leaves, however, the unsatisfactory requirement of choosing a penalty parameter λ with its recommended setting λ = 1600 (see also Schlicht 2005 or Harvey and Jaeger 1993 for a data driven selection of λ). We therefore make use of the proposed penalized spline filter by Kauermann et al (2011), see also Paige and Trindade (2010). We therefore rewrite (2.10) to…”

Section: Filtering the Long Phase Structurementioning

confidence: 99%

“…The separation of long term and short term fluctuation seems more or less adequate for the data. The smoothing parameters for the long term trend are thereby selected based on Maximum Likelihood theory following Kauermann et al (2011). Looking now at the short term cycle g(t) given in Fig.…”

Section: Simulationmentioning

confidence: 99%

“…Instead, we also make use of penalized splines to estimate the long term trend c(t). Kauermann et al (2011) show the practicability of penalized spline smoothing for filtering time series. In particular, they compare a penalized spline filter to the above mentioned competitors, namely the HP-filter and the bandpass filter, see also Paige and Trindade (2010).…”

Section: Introductionmentioning

confidence: 96%

“…Although the choices of these parameters are (subjectively) reasoned we again warn to follow this suggestions blindly. A statistical approach which selects the tuning parameter data driven is suggested in the paper, see also Kauermann et al (2011).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exploring US Business Cycles with Bivariate Loops Using Penalized Spline Regression

2011

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The phrase business cycle is usually used for short term fluctuations in macroeconomic time series. In this paper we focus on the estimation of business cycles in a bivariate manner by fitting two series simultaneously. The underlying model is thereby nonparametric in that no functional form is prespecified but smoothness of the functions are assumed. The functions are then estimated using penalized spline estimation. The bivariate approach will allow to compare business cycles, check and compare phase lengths and visualize this in forms of loops in a bivariate way. Moreover, the focus is on separation of long and short phase fluctuation, where only the latter is the classical business cycle while the first is better known as Friedman or Goodwin cycle, respectively. Again, we use nonparametric models and fit the functional shape with penalized splines. For the separation of long and short phase components we employ an Akaike criterion.

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Practical Smoothing

Eilers

Marx

2021

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This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends these attractive properties to multiple dimensions. An appendix offers a systematic comparison to other smoothers.

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Filtering Time Series with Penalized Splines

Cited by 12 publications

References 34 publications

L- and V-curves for optimal smoothing

L- and V-curves for optimal smoothing

Exploring US Business Cycles with Bivariate Loops Using Penalized Spline Regression

Practical Smoothing

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