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  • Irma Hindrayanto (a1), Jan P.A.M. Jacobs (a2), Denise R. Osborn (a3) and Jing Tian (a4)

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.

Corresponding author
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:
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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.

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Abeln, Barend and Jacobs, Jan P. A. M. (2016) CAMPLET: Seasonal adjustment without revisions. Presented at Joint Statistical Meetings 2016. Chicago, IL.
Anderson, Brian D. O. and Moore, John B. (1979) Optimal Filtering. Englewood Cliffs: Prentice-Hall.
Anderson, Heather, Low, Chian Nam, and Snyder, Ralph (2006) Single source of error state space approach to the Beveridge–Nelson decomposition. Economics Letters 91, 104109.
Barsky, Robert B. and Miron, Jeffrey A. (1989) The seasonal cycle and the business cycle. Journal of Political Economy 97, 503534.
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, 621656.
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, 151174.
Canova, Fabio and Ghysels, Eric (1994) Changes in seasonal patterns: Are they cyclical? Journal of Economic Dynamics and Control 18, 11431171.
Cecchetti, Stephen G. and Kashyap, Anil K. (1996) International cycles. European Economic Review 40, 331360.
Clark, Peter K. (1987) The cyclical component of U.S. economic activity. Quarterly Journal of Economics 102, 797814.
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, 661692.
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, 15131527.
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, 776790.
Durbin, James and Koopman, Siem Jan (2012) Time Series Analysis by State Space Methods, 2nd ed. Oxford: Oxford University Press.
Engle, Robert F. (1978) Estimating structural models of seasonality. In Zellner, Arnold, (ed.), Seasonal Analysis of Economic Time Series, pp. 281308. Washington DC: Bureau of the Census.
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.
Grether, D. M. and Nerlove, M. (1970) Some properties of ‘optimal’ seasonal adjustment. Econometrica 38, 682703.
Hamilton, James D. (1994) Time Series Analysis. Princeton: Princeton University Press.
Hamilton, James D. (2017) Why you should never use the Hodrick–Prescott filter. Review of Economics and Statistics (forthcoming).
Harvey, Andrew C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge, UK: Cambridge University Press.
Harvey, Andrew C. (1990) The Econometric Analysis of Time Series. Cambridge, MA: MIT Press.
Hylleberg, Svend, Engle, Robert F., Granger, Clive W. J., and Yoo, Byung Sam (1990) Seasonal integration and cointegration. Journal of Econometrics 44, 215238.
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, 427448.
Krane, Spencer and Wascher, William (1999) The cyclical sensitivity of seasonality in U.S. employment. Journal of Monetary Economics 44, 523553.
Lütkepohl, Helmut (1984). Linear transformations of vector ARMA processes. Journal of Econometrics 26, 283293.
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.
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, 13091332.
McElroy, Tucker S. and Maravall, Agustin (2014) Optimal signal extraction with correlated components. Journal of Time Series Econometrics 6, 237273.
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, 235243.
Morley, James C. and Piger, Jeremy (2012) The asymmetric business cycle. Review of Economics and Statistics 94, 208221.
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, 361377.
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, 16211629.
Proietti, Tomasso (2006) Trend–cycle decompositions with correlated components. Econometric Reviews 25, 6184.
Sinclair, Tara M. (2010) Asymmetry in the business cycle: Friedman's plucking model with correlated innovations. Studies in Nonlinear Dynamics and Econometrics 14, 235243.
Stock, James H (2013) Comments on Unseasonal Seasonals? Brookings Papers on Economic Activity Fall, 111–119.
Wada, Tatsuma (2012) On the correlations of trend–cycle errors. Economics Letters 116, 396400.
Weber, Enzo (2011) Analyzing U.S. output and the Great Moderation by simultaneous unobserved components. Journal of Money, Credit and Banking 43, 15791597.
Wright, Jonathan H. (2013) Unseasonal seasonals? (Including comments and discussion). Brookings Papers on Economic Activity Fall, 65–126.
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Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
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