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The Sources and Nature of Long-term Memory in the Business Cycle

  • Joseph G. Haubrich
  • Andrew W. Lo

This paper examines the stochastic properties of aggregate macroeconomic time series from the standpoint of fractionally integrated models, and focuses on the persistence of economic shocks. We develop a simple macroeconomic model that exhibits long-term dependence, a consequence of aggregation in the presence of real business cycles. We derive the relation between properties of fractionally integrated macroeconomic time series and those of microeconomic data, and discuss how fiscal policy may alter their stochastic behavior. To implement these results empirically, we employ a test for fractionally integrated time series based on the Hurst-Mandelbrot rescaled range. This test is robust to short-term dependence, and is applied to quarterly and annual real GNP to determine the sources and nature of long-term dependence in the business cycle.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 2951.

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Date of creation: Apr 1989
Date of revision:
Publication status: published as Haubrich, Joseph G. and Andrew W. Lo. "The Sources And Nature Of Long-Term Memory In Aggregate Output," FRB Cleveland - Economic Review, 2001, v37(2,Second-Qtr), 15-30.
Handle: RePEc:nbr:nberwo:2951
Note: ME
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  1. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
  2. Danny Quah, 1987. "What Do We Learn from Unit Roots in Macroeconomic Time Series?," Working papers 469, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
  4. Baxter, Marianne, 1991. "Approximating suboptimal dynamic equilibria : An Euler equation approach," Journal of Monetary Economics, Elsevier, vol. 28(2), pages 173-200, October.
  5. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-51, May.
  6. Francis X. Diebold & Glenn D. Rudebusch, 1988. "Long memory and persistence in aggregate output," Finance and Economics Discussion Series 7, Board of Governors of the Federal Reserve System (U.S.).
  7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  8. Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
  9. Sowell, F., 1989. "The Deterministic Trend In Real Gnp," GSIA Working Papers 88-89-60, Carnegie Mellon University, Tepper School of Business.
  10. Campbell, John & Mankiw, Gregory, 1987. "Are Output Fluctuations Transitory?," Scholarly Articles 3122545, Harvard University Department of Economics.
  11. Jeremy Greenwood & Gregory W. Huffman, 1991. "Tax analysis in a real business cycle model: on measuring Harberger triangles and Okun gaps," Staff Report 138, Federal Reserve Bank of Minneapolis.
  12. Paul M Romer, 1999. "Increasing Returns and Long-Run Growth," Levine's Working Paper Archive 2232, David K. Levine.
  13. 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.
  14. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  15. Perron, P. & Phillips, P.C.B., 1986. "Does Gnp Have a Unit Root? a Reevaluation," Cahiers de recherche 8640, Universite de Montreal, Departement de sciences economiques.
  16. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
  17. Stock, James H. & Watson, Mark W., 1986. "Does GNP have a unit root?," Economics Letters, Elsevier, vol. 22(2-3), pages 147-151.
  18. Singleton, Kenneth J., 1988. "Econometric issues in the analysis of equilibrium business cycle models," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 361-386.
  19. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
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