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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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  • Charles R. Nelson

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.

Suggested Citation

  • Charles R. Nelson, 1987. "Spurious Trend and Cycle in the State Space Decomposition of a Time Series with a Unit Root," NBER Technical Working Papers 0063, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0063
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    1. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-751, May.
    2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    3. Beveridge, Stephen & 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, Elsevier, vol. 7(2), pages 151-174.
    4. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
    5. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    6. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    7. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 797-814.
    8. Harvey, A C & Todd, P H J, 1983. "Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 299-307, October.
    9. Harvey, A C & Todd, P H J, 1983. "Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study: Response," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 313-315, October.
    10. Charles R. Nelson, 1987. "Implicit Estimates of Natural, Trend, and Cyclical Components of Real GNP," NBER Working Papers 2253, National Bureau of Economic Research, Inc.
    11. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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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. Bomhoff, E.J., 1991. "Stability of Velocity in the G-7 Countries : A Kalman Filter Approach," Discussion Paper 1991-18, Tilburg University, Center for Economic Research.
    7. 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.
    8. Deryugina, Elena & Ponomarenko, Alexey & Rozhkova, Anna, 2020. "When are credit gap estimates reliable?," Economic Analysis and Policy, Elsevier, vol. 67(C), pages 221-238.
    9. Andrew E. Evans, 2020. "Average labour productivity dynamics over the business cycle," Empirical Economics, Springer, vol. 59(4), pages 1833-1863, October.
    10. 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.
    11. 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.
    12. 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.
    13. Jacky Fayolle, 1993. "Décrire le cycle économique," Revue de l'OFCE, Programme National Persée, vol. 45(1), pages 161-197.
    14. Cribari-Neto, Francisco, 1993. "The Cyclical Component in Brazilian GDP," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 13(1), April.
    15. Heejoon Kang, 2004. "Inappropriate Detrending and Spurious Cointegration," Econometric Society 2004 Far Eastern Meetings 624, Econometric Society.
    16. 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.
    17. repec:dau:papers:123456789/12185 is not listed on IDEAS
    18. D., Ivan, 2017. "Stability of the labour shares: evidence from OECD economies," MPRA Paper 79822, University Library of Munich, Germany.
    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, June.
    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.

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