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A Heuristic Method for Extracting Smooth Trends from Economic Time Series

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  • Julio J. Rotemberg

Abstract

This paper proposes a method for separating economic time series into a smooth component whose mean varies over time (the trend') and a stationary component (the cycle'). The aim is to make the trends as smooth as possible while also producing cycles with plausible properties. While the main justification for the method is intuitive, the method does a good job of separating these two components in some artificial examples where the constructed series are indeed the sum of smooth (possibly stochastic) functions of time and a low order autoregressive process. When the true trends consist of low order polynomials, the proposed method obtains trends that are of similar accuracy than fitted polynomial trends. In other cases, the MSE of the proposed trends is much lower. Similarly, except in quite special cases, the MSE of the proposed trend is considerably smaller than that obtained by the HP filter. VARs that involve the cyclical variables constructed by this method yield accurate representations of the behavior of the underlying cycles of several variables. By contrast, VARs with the series in differences give poor descriptions of the effect of cyclical shocks, even though Dickey-Fuller tests do not reject the hypotheses that the artificial series have unit roots. I apply the method to some well known aggregate time series. The results suggest that real wages in the U.S. are strongly positively correlated with military purchases and that the reduction in the growth of trend GDP in the U.S. started well before 1973.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 7439.

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Date of creation: Dec 1999
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Handle: RePEc:nbr:nberwo:7439

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Cited by:
  1. Julio J. Rotemberg, 2003. "Stochastic Technical Progress, Smooth Trends, and Nearly Distinct Business Cycles," American Economic Review, American Economic Association, vol. 93(5), pages 1543-1559, December.
  2. Athanasios Orphanides & John C. Williams, 2002. "Robust Monetary Policy Rules with Unknown Natural Rates," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 33(2), pages 63-146.
  3. Lars Calmfors & Giancarlo Corsetti & Seppo Honkapohja & John Kay & Gilles Saint-Paul & Hans-Werner Sinn & Jan-Egbert Sturm & Xavier Vives, 2006. "Chapter 1: The European Economy: Macroeconomic Outlook and Policy," EEAG Report on the European Economy, CESifo Group Munich, vol. 0, pages 12-49, 03.
  4. Arby, Muhammad Farooq, 2001. "Long-run trend, Business Cycle & Short-run shocks in real GDP," MPRA Paper 4929, University Library of Munich, Germany.
  5. Lastrapes, W.D., 2000. "Real Wages and Aggregate Demand Shocks: Contradictory Evidence from Vars," Papers 99-476, Georgia - College of Business Administration, Department of Economics.
  6. Julio J. Rotemberg, 2005. "Commentary on "reexamining the monetarist critique of interest rate rule"," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 531-536.
  7. Jorge Enrique Restrepo & Claudio Soto, 2004. "Regularidades Empíricas de la Economía Chilena," Working Papers Central Bank of Chile 301, Central Bank of Chile.
  8. Julio J. Rotemberg, 2007. "Minimally altruistic wages and unemployment in a matching model," Working Papers 07-5, Federal Reserve Bank of Boston.
  9. Zarnowitz, Victor & Ozyildirim, Ataman, 2006. "Time series decomposition and measurement of business cycles, trends and growth cycles," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1717-1739, October.
  10. Lucas Navarro & Raimundo Soto, 2006. "Procyclical Productivity in Manufacturing," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 43(127), pages 193-220.
  11. Harm Bandholz & Gebhard Flaig & Johannes Mayr, 2005. "Wachstum und Konjunktur in OECD-Ländern: Eine langfristige Perspektive," Ifo Schnelldienst, Ifo Institute for Economic Research at the University of Munich, vol. 58(04), pages 28-36, 02.
  12. Gebhard Flaig, 2001. "Trend and Cycles in U.S. Real GDP," CESifo Working Paper Series 607, CESifo Group Munich.
  13. McKay, Alisdair & Reis, Ricardo, 2006. "The Brevity and Violence of Contractions and Expansions," CEPR Discussion Papers 5756, C.E.P.R. Discussion Papers.
  14. Gebhard Flaig & Timo Wollmershäuser, 2007. "Does the Euro-zone Diverge? A Stress Indicator for Analyzing Trends and Cycles in Real GDP and Inflation," CESifo Working Paper Series 1937, CESifo Group Munich.

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