Seasonality with trend and cycle interactions in unobserved components models
AbstractUnobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, which is often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear-additive framework may be too restrictive. We formulate a non-linear unobserved components time series model which allows interactions between the trend-cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle-dependent seasonal fluctuations. Copyright (c) 2009 Royal Statistical Society.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series C (Applied Statistics).
Volume (Year): 58 (2009)
Issue (Month): 4 ()
Contact details of provider:
Postal: 12 Errol Street, London EC1Y 8LX, United Kingdom
Web page: http://www.blackwellpublishing.com/journal.asp?ref=0035-9254
More information through EDIRC
Other versions of this item:
- Siem Jan Koopman & Kai Ming Lee, 0000. "Seasonality with Trend and Cycle Interactions in Unobserved Components Models," Tinbergen Institute Discussion Papers 08-028/4, Tinbergen Institute.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
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.:
- Commandeur, Jacques J.F. & Koopman, Siem Jan, 2007. "An Introduction to State Space Time Series Analysis," OUP Catalogue, Oxford University Press, number 9780199228874.
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543.
- Tom Doan, . "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- Harvey, Andrew & Scott, Andrew, 1994.
"Seasonality in Dynamic Regression Models,"
Royal Economic Society, vol. 104(427), pages 1324-45, November.
- Franses, Philip Hans, 1995. "Quarterly US Unemployment: Cycles, Seasons and Asymmetries," Empirical Economics, Springer, vol. 20(4), pages 717-25.
- 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.
- D R Osborn & A Matas-Mir, 2001.
"Does Seasonality Change over the Business Cycle? An Investigation using Monthly Industrial Production Series,"
Centre for Growth and Business Cycle Research Discussion Paper Series
09, Economics, The Univeristy of Manchester.
- Matas-Mir, Antonio & Osborn, Denise R., 2004. "Does seasonality change over the business cycle? An investigation using monthly industrial production series," European Economic Review, Elsevier, vol. 48(6), pages 1309-1332, December.
- Matas-Mir, Antoni & Denise R Osborn, 2002. "Does Seasonality Change over the Business Cycle? An Investigation using Monthly Industrial Production Series," Royal Economic Society Annual Conference 2002 139, Royal Economic Society.
- A Matas-Mir & D R Osborn, 2001. "Does Seasonality Change Over the Business Cycle? An Investigation Using Monthly Industrial Production Series," The School of Economics Discussion Paper Series 0110, Economics, The University of Manchester.
- [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
- J. Durbin & S. J. Koopman, 2000.
"Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives,"
Journal of the Royal Statistical Society Series B,
Royal Statistical Society, vol. 62(1), pages 3-56.
- Durbin, J. & Koopman, S.J.M., 1998. "Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives," Discussion Paper 1998-142, Tilburg University, Center for Economic Research.
- Stephen G. Cecchetti & Anil K. Kashyap & David W. Wilcox, 1997.
"Interactions between the seasonal and business cycles in production and inventories,"
Working Paper Series, Macroeconomic Issues
WP-97-06, Federal Reserve Bank of Chicago.
- Cecchetti, Stephen G & Kashyap, Anil K & Wilcox, David W, 1997. "Interactions between the Seasonal and Business Cycles in Production and Inventories," American Economic Review, American Economic Association, vol. 87(5), pages 884-92, December.
- Gersch, Will & Kitagawa, Genshiro, 1983. "The Prediction of Time Series with Trends and Seasonalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 253-64, July.
- S. J. Koopman & J. Durbin, 2003. "Filtering and smoothing of state vector for diffuse state-space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 85-98, 01.
- Franses, Ph.H.B.F. & Bruin, P. de, 1999. "Seasonal adjustment and the business cycle in unemployment," Econometric Institute Report EI 9923-/A, Erasmus University Rotterdam, Econometric Institute.
- Tommaso Proietti & Marco Riani, 2009. "Transformations and seasonal adjustment," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 47-69, 01.
- repec:fth:erroem:9923/a is not listed on IDEAS
- Steven Clark & T. Coggin, 2009. "Trends, Cycles and Convergence in U.S. Regional House Prices," The Journal of Real Estate Finance and Economics, Springer, vol. 39(3), pages 264-283, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.