Transformations and Seasonal Adjustment: Analytic Solutions and Case Studies
AbstractWe address the problem of seasonal adjustment of a nonlinear transformation of the original time series, such as the Box-Cox transformation of a time series measured on a ratio scale, or the Aranda-Ordaz transformation of proportions, which aims at enforcing two essential features: additivity and orthogonality of the components. The posterior mean and variance of the seasonally adjusted series admit an analytic finite representation only for particular values of the transformation parameter, e.g. for a fractional Box-Cox transformation parameter. Even if available, the analytical derivation can be tedious and difficult. As an alternative we propose to compute the two conditional moments of the seasonally adjusted series by means of numerical and Monte Carlo integration. The former is both fast and reliable in univariate applications. The latter uses the algorithm known as the simulation smoother and it is most useful in multivariate applications. We present several case studies dealing with robust seasonal adjustment under the square root and the fourth root transformation, the seasonal adjustment of the ratio of two series, and the adjustment of time series of proportions. Our overall conclusion is that robust seasonal adjustment under transformations can be carried out routinely and that the possibility of transforming the scale ought to be considered as a further option for improving the quality of seasonal adjustment.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 7862.
Date of creation: 03 Dec 2007
Date of revision:
Structural Time Series Models; Box-Cox Transformation; Aranda–Ordaz Transformation; Simulation Smoother; Forward Search; Numerical Integration;
Find related papers by JEL classification:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-03-25 (All new papers)
- NEP-ECM-2008-03-25 (Econometrics)
- NEP-ORE-2008-03-25 (Operations Research)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Riani Marco, 2004. "Extensions of the Forward Search to Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.
- Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999.
"Statistical algorithms for models in state space using SsfPack 2.2,"
Royal Economic Society, vol. 2(1), pages 107-160.
- Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
- Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
- Harvey, Andrew & Proietti, Tommaso (ed.), 2005. "Readings in Unobserved Components Models," OUP Catalogue, Oxford University Press, number 9780199278695, September.
- [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
- Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-52, April.
- Victor Gómez & Agustín Maravall, 1996. "Programs TRAMO and SEATS, Instruction for User (Beta Version: september 1996)," Banco de Espaï¿½a Working Papers 9628, Banco de Espa�a.
- Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
- Santiago Cajiao Raigosa & Luis Fernando Melo Velandia & Daniel Parra Amado, 2014.
"Pronósticos para una economía menos volátil: El caso colombiano,"
BORRADORES DE ECONOMIA
011252, BANCO DE LA REPÚBLICA.
- Santiago Cajiao Raigosa & Luis Fernando Melo Velandia & Daniel Parra Amado, 2014. "Pronósticos para una economía menos volátil: El caso colombiano," Borradores de Economia 821, Banco de la Republica de Colombia.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.