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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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0063.

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Date of creation: Nov 1987
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Publication status: published as Journal of Economic Dynamics and Control, vol. 12,no.2/3, June/September 1988, pp475-488.
Handle: RePEc:nbr:nberte:0063

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  1. 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.
  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 1057-72, June.
  3. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-51, May.
  4. 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.
  5. Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 797-814, November.
  6. 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.
  7. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
  8. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
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Cited by:
  1. repec:dau:papers:123456789/12185 is not listed on IDEAS
  2. Santiago Herrera, 2000. "Determinantes y Composici├│n del Endeudamiento P├║blico en Colombia," Research Department Publications 3105, Inter-American Development Bank, Research Department.
  3. 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.
  4. Heejoon Kang, 2004. "Inappropriate Detrending and Spurious Cointegration," Econometric Society 2004 Far Eastern Meetings 624, Econometric Society.
  5. Ndiaye, Cheikh Tidiane & Bates, Samuel, 2014. "Economic Growth from a Structural Unobserved Component Modeling: The Case of Senegal," Economics Papers from University Paris Dauphine 123456789/13298, Paris Dauphine University.
  6. 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.
  7. 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.
  8. 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.

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