Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T21:13:58.830Z Has data issue: false hasContentIssue false
  • English
  • Français

TREND–CYCLE–SEASONAL INTERACTIONS: IDENTIFICATION AND ESTIMATION

Published online by Cambridge University Press:  06 February 2018

Irma Hindrayanto ,
Jan P.A.M. Jacobs ,
Denise R. Osborn  and
Jing Tian
Irma Hindrayanto
Affiliation:
De Nederlandsche Bank
Jan P.A.M. Jacobs*
Affiliation:
University of Groningen, University of Tasmania, CAMA, and CIRANO
Denise R. Osborn
Affiliation:
University of Manchester, University of Tasmania, and CAMA
Jing Tian
Affiliation:
University of Tasmania
*
Address correspondence to: Jan P.A.M. Jacobs, Faculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, the Netherlands; e-mail: j.p.a.m.jacobs@rug.nl.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits nonzero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

Keywords

Trend–Cycle–Seasonal DecompositionUnobserved ComponentsSeasonal AdjustmentEmploymentGreat Recession
Type
Articles
Information
Macroeconomic Dynamics , Volume 23 , Issue 8 , December 2019 , pp. 3163 - 3188
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2018

Footnotes

We thank Siem Jan Koopman and Kai Ming Lee for helpful discussions. We also thank Ralph Snyder, Ken Wallis, Tom Wansbeek, William A. Barnett, and an associate editor for detailed comments on a previous version of the paper. However, any errors are entirely the responsibility of the authors. Views expressed in this paper do not necessarily reflect those of the Dutch Central Bank.

References

REFERENCES

Abeln, Barend and Jacobs, Jan P. A. M. (2016) CAMPLET: Seasonal adjustment without revisions. Presented at Joint Statistical Meetings 2016. Chicago, IL.Google Scholar
Anderson, Brian D. O. and Moore, John B. (1979) Optimal Filtering. Englewood Cliffs: Prentice-Hall.Google Scholar
Anderson, Heather, Low, Chian Nam, and Snyder, Ralph (2006) Single source of error state space approach to the Beveridge–Nelson decomposition. Economics Letters 91, 104–109.Google Scholar
Barsky, Robert B. and Miron, Jeffrey A. (1989) The seasonal cycle and the business cycle. Journal of Political Economy 97, 503–534.Google Scholar
Beaulieu, J. Joseph, MacKie-Mason, Jeffrey K., and Miron, Jeffrey A. (1992) Why do countries and industries with large seasonal cycles also have large business cycles? Quarterly Journal of Economics 107, 621–656.Google Scholar
Beveridge, Stephen and Nelson, Charles R. (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cycle’. Journal of Monetary Economics 7, 151–174.Google Scholar
Canova, Fabio and Ghysels, Eric (1994) Changes in seasonal patterns: Are they cyclical? Journal of Economic Dynamics and Control 18, 1143–1171.Google Scholar
Cecchetti, Stephen G. and Kashyap, Anil K. (1996) International cycles. European Economic Review 40, 331–360.Google Scholar
Clark, Peter K. (1987) The cyclical component of U.S. economic activity. Quarterly Journal of Economics 102, 797–814.Google Scholar
Davidson, James E. H., Hendry, David F., Srba, Frank, and Yeo, Stephen (1978) Econometric modelling of the aggregate time-series relationship between consumers' expenditure and income in the United Kingdom. The Economic Journal 88, 661–692.Google Scholar
De Livera, Alysha M., Hyndman, Rob J., and Snyder, Ralph D. (2011) Forecasting time series with complex seasonal patterns using exponential smoothing. Journal of the American Statistical Association 106, 1513–1527.Google Scholar
Dungey, Mardi, Jacobs, Jan P. A. M., Tian, Jing, and van Norden, Simon (2015) Trend in cycle or cycle in trend? New structural identifications for unobserved components models of U.S. real GDP. Macroeconomic Dynamics 19, 776–790.Google Scholar
Durbin, James and Koopman, Siem Jan (2012) Time Series Analysis by State Space Methods, 2nd ed. Oxford: Oxford University Press.Google Scholar
Engle, Robert F. (1978) Estimating structural models of seasonality. In Zellner, Arnold, (ed.), Seasonal Analysis of Economic Time Series, pp. 281–308. Washington DC: Bureau of the Census.Google Scholar
Evans, Thomas D. and Tiller, Richard B. (2013) Seasonal adjustment of CPS labor force series during the great recession. In Proceedings of the 2013 Joint Statistical Meetings, Business and Economics Section. American Statistical Association.Google Scholar
Grether, D. M. and Nerlove, M. (1970) Some properties of ‘optimal’ seasonal adjustment. Econometrica 38, 682–703.Google Scholar
Hamilton, James D. (1994) Time Series Analysis. Princeton: Princeton University Press.Google Scholar
Hamilton, James D. (2017) Why you should never use the Hodrick–Prescott filter. Review of Economics and Statistics (forthcoming).Google Scholar
Harvey, Andrew C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge, UK: Cambridge University Press.Google Scholar
Harvey, Andrew C. (1990) The Econometric Analysis of Time Series. Cambridge, MA: MIT Press.Google Scholar
Hylleberg, Svend, Engle, Robert F., Granger, Clive W. J., and Yoo, Byung Sam (1990) Seasonal integration and cointegration. Journal of Econometrics 44, 215–238.Google Scholar
Koopman, Siem Jan and Lee, Kai Ming (2009) Seasonality with trend and cycle interactions in unobserved components models. Journal of the Royal Statistical Society Series C 58, 427–448.Google Scholar
Krane, Spencer and Wascher, William (1999) The cyclical sensitivity of seasonality in U.S. employment. Journal of Monetary Economics 44, 523–553.Google Scholar
Lütkepohl, Helmut (1984). Linear transformations of vector ARMA processes. Journal of Econometrics 26, 283–293.Google Scholar
Lytras, Demetra and Bell, William R. (2013) Modeling recession effects and the consequences on seasonal adjustment. In Proceedings of the 2013 Joint Statistical Meetings, Business and Economics Section. American Statistical Association.Google Scholar
Matas-Mir, Antonio and Osborn, Denise R. (2004) Does seasonality change over the business cycle? An investigation using monthly industrial production series. European Economic Review 48, 1309–1332.Google Scholar
McElroy, Tucker S. and Maravall, Agustin (2014) Optimal signal extraction with correlated components. Journal of Time Series Econometrics 6, 237–273.Google Scholar
Morley, James C., Nelson, Charles R., and Zivot, Eric (2003) Why are the Beveridge–Nelson and unobserved-components decompositions of GDP so different? Review of Economics and Statistics 85, 235–243.Google Scholar
Morley, James C. and Piger, Jeremy (2012) The asymmetric business cycle. Review of Economics and Statistics 94, 208–221.Google Scholar
Osborn, Denise R., Chui, A. P. L., Smith, Jeremy P., and Birchenhall, C. R. (1988) Seasonality and the order of integration for consumption. Oxford Bulletin of Economics and Statistics 50, 361–377.Google Scholar
Ord, J. Keith, Koehler, Anne B., and Snyder, Ralph D. (1997) Estimation and prediction for a class of dynamic nonlinear statistical models. Journal of the American Statistical Association 92, 1621–1629.Google Scholar
Proietti, Tomasso (2006) Trend–cycle decompositions with correlated components. Econometric Reviews 25, 61–84.Google Scholar
Sinclair, Tara M. (2010) Asymmetry in the business cycle: Friedman's plucking model with correlated innovations. Studies in Nonlinear Dynamics and Econometrics 14, 235–243.Google Scholar
Stock, James H (2013) Comments on Unseasonal Seasonals? Brookings Papers on Economic Activity Fall, 111–119.Google Scholar
Wada, Tatsuma (2012) On the correlations of trend–cycle errors. Economics Letters 116, 396–400.Google Scholar
Weber, Enzo (2011) Analyzing U.S. output and the Great Moderation by simultaneous unobserved components. Journal of Money, Credit and Banking 43, 1579–1597.Google Scholar
Wright, Jonathan H. (2013) Unseasonal seasonals? (Including comments and discussion). Brookings Papers on Economic Activity Fall, 65–126.Google Scholar