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Spurious trend and cycle in the state space decomposition of a time series with a unit root

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  • Nelson, Charles R.

Abstract

Recent research has proposed the state space (88) framework for decomposition of GNP and other economic time series into trend and cycle components, using the Kalman filter. This paper reviews the empirical evidence and suggests that the resulting decomposition may be spurious, just as detrending by linear regression is known to generate spurious trends and cycles in nonstationary time series. A Monte Carlo experiment confirms that when data is generated by a random walk, the 88 model tends to indicate (incorrectly) that the series consists of cyclical variations around a smooth trend. The improvement in fit over the true model will typically appear to be statistically significant. These results suggest that caution should be exercised in drawing inferences about the nature of economic processes from the 88 decomposition.
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Suggested Citation

  • Nelson, Charles R., 1988. "Spurious trend and cycle in the state space decomposition of a time series with a unit root," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 475-488.
    • Handle: RePEc:eee:dyncon:v:12:y:1988:i:2-3:p:475-488
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    Cited by:

    1. Herrera, Santiago, 2000. "Determinantes y composición del endeudamiento público en Colombia," IDB Publications (Working Papers) 2110, Inter-American Development Bank.
    2. Kim Chung-Han, 2000. "Balassa-Samuelson Theory and Predictability of the US/UK Real Exchange Rate," International Economic Journal, Taylor & Francis Journals, vol. 14(3), pages 101-121.
    3. José Luis Cendejas & Félix-Fernando Muñoz & Nadia Fernández-de-Pinedo, 2017. "A contribution to the analysis of historical economic fluctuations (1870–2010): filtering, spurious cycles, and unobserved component modeling," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 11(1), pages 93-125, January.
    4. Elena Deryugina & Alexey Ponomarenko, 2020. "Disinflation and Reliability of Underlying Inflation Measures," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(1), pages 91-111, March.
    5. Samuel Bates & Cheikh Tidiane Ndiaye, 2014. "Economic Growth from a Structural Unobserved Component Modeling: The Case of Senegal," Economics Bulletin, AccessEcon, vol. 34(2), pages 951-965.
    6. Deryugina, Elena & Ponomarenko, Alexey & Rozhkova, Anna, 2020. "When are credit gap estimates reliable?," Economic Analysis and Policy, Elsevier, vol. 67(C), pages 221-238.
    7. Andrew E. Evans, 2020. "Average labour productivity dynamics over the business cycle," Empirical Economics, Springer, vol. 59(4), pages 1833-1863, October.
    8. Drew Creal & Siem Jan Koopman & Eric Zivot, 2010. "Extracting a robust US business cycle using a time-varying multivariate model-based bandpass filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 695-719.
    9. Eduard J. Bomhoff, 1991. "Stability of Velocity in the Major Industrial Countries: A Kalman Filter Approach," IMF Staff Papers, Palgrave Macmillan, vol. 38(3), pages 626-642, September.
    10. Ivan D. Trofimov, 2019. "Stability of Labour Shares: Evidence from OECD Economies," South-Eastern Europe Journal of Economics, Association of Economic Universities of South and Eastern Europe and the Black Sea Region, vol. 17(1), pages 57-89.
    11. Jacky Fayolle, 1993. "Décrire le cycle économique," Revue de l'OFCE, Programme National Persée, vol. 45(1), pages 161-197.
    12. Bomhoff, E.J., 1991. "Stability of Velocity in the G-7 Countries : A Kalman Filter Approach," Other publications TiSEM 7e0b8fb6-7196-4519-9c82-f, Tilburg University, School of Economics and Management.
    13. Cribari-Neto, Francisco, 1993. "The Cyclical Component in Brazilian GDP," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 13(1), April.
    14. Heejoon Kang, 2004. "Inappropriate Detrending and Spurious Cointegration," Econometric Society 2004 Far Eastern Meetings 624, Econometric Society.
    15. Marta Skrzypczyńska, 2014. "Cyclical Processes in the Polish Economy," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(3), pages 153-192, September.
    16. repec:dau:papers:123456789/12185 is not listed on IDEAS
    17. D., Ivan, 2017. "Stability of the labour shares: evidence from OECD economies," MPRA Paper 79822, University Library of Munich, Germany.
    18. Jun Ma & Charles R. Nelson, 2008. "Valid Inference for a Class of Models Where Standard Inference Performs Poorly: Including Nonlinear Regression, ARMA, GARCH, and Unobserved Components," Working Papers UWEC-2008-06-R, University of Washington, Department of Economics, revised Sep 2008.
    19. Schüler, Yves S., 2018. "Detrending and financial cycle facts across G7 countries: mind a spurious medium term!," Working Paper Series 2138, European Central Bank.
    20. Luis Lorente, 1991. "Políticas monetarias e inflación, Colombia 1951-1989," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID.
    21. Santiago Herrera, 2000. "Determinantes y Composición del Endeudamiento Público en Colombia," Research Department Publications 3105, Inter-American Development Bank, Research Department.
    22. Catherine Doz & Guillaume Rabault & Nicolas Sobczak, 1995. "Décomposition tendance-cycle : estimations par des méthodes statistiques univariées," Économie et Prévision, Programme National Persée, vol. 120(4), pages 73-93.
    23. José Cendejas Bueno & Cecilia Font de Villanueva, 2015. "Convergence of inflation with a common cycle: estimating and modelling Spanish historical inflation from the 16th to the 18th centuries," Empirical Economics, Springer, vol. 48(4), pages 1643-1665, June.
    24. J. Bradford De Long & Lawrence H. Summers, 1988. "On the Existence and Interpretation of the "Unit Root" in U.S. GNP," NBER Working Papers 2716, National Bureau of Economic Research, Inc.
    25. Fève, Patrick & Moura, Alban, 2025. "Measuring business cycles using vars," TSE Working Papers 25-1673, Toulouse School of Economics (TSE).

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