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

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  • Joseph G. Haubrich
  • Andrew W. Lo

Abstract

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.

Suggested Citation

  • Joseph G. Haubrich & Andrew W. Lo, 1989. "The Sources and Nature of Long-term Memory in the Business Cycle," NBER Working Papers 2951, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:2951
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    1. West, Kenneth D. & Cho, Dongchul, 1995. "The predictive ability of several models of exchange rate volatility," Journal of Econometrics, Elsevier, vol. 69(2), pages 367-391, October.
    2. Aloy, Marcel & Boutahar, Mohamed & Gente, Karine & Péguin-Feissolle, Anne, 2011. "Purchasing power parity and the long memory properties of real exchange rates: Does one size fit all?," Economic Modelling, Elsevier, vol. 28(3), pages 1279-1290, May.
    3. Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June.
    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    5. Peter C.B. Phillips & Mico Loretan, 1990. "Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns," Cowles Foundation Discussion Papers 947, Cowles Foundation for Research in Economics, Yale University.
    6. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    7. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    8. Haubrich, Joseph G, 1993. "Consumption and Fractional Differencing: Old and New Anomalies," The Review of Economics and Statistics, MIT Press, vol. 75(4), pages 767-772, November.
    9. Silverberg, Gerald & Verspagen, Bart, 1999. "Long Memory in Time Series of Economic Growth and Convergence," Research Memorandum 015, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    10. B. Verspagen & G. Silverberg, 2000. "A note on Michelacci and Zaffaroni, long memory, and time series of economic growth," Working Papers 00.17, Eindhoven Center for Innovation Studies.
    11. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    12. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    13. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    14. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
    15. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
    16. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
    17. Dominique, C-René & Rivera-Solis, Luis Eduardo, 2011. "Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index," MPRA Paper 34860, University Library of Munich, Germany.
    18. Mehmet Balcilar, 2004. "Persistence in Inflation: Does Aggregation Cause Long Memory?," Emerging Markets Finance and Trade, M.E. Sharpe, Inc., vol. 40(5), pages 25-56, September.
    19. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    20. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.

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