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Measuring persistence in aggregate output: ARMA models, fractionally integrated ARMA models and nonparametric procedures

Author

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  • Erhard Reschenhofer

    (Institut für Statistik, Universität Wien, Universitätsstrasse 5, A-1010 Vienna, Austria)

  • Benedikt M. Pötscher

    (Institut für Statistik, Universität Wien, Universitätsstrasse 5, A-1010 Vienna, Austria)

  • Michael A. Hauser

    (Institut für Statistik, Wirtschaftsuniversität Wien, Augasse 2-6, A-1090 Vienna, Austria)

Abstract

Econometric issues in the estimation of persistence in macroeconomic time series are considered. In particular, the relative merits of estimates based on ARMA models, ARFIMA models and nonparametric procedures are investigated. It is shown that ARFIMA models are inappropriate for the purpose of estimating persistence. Furthermore, some of the criticism leveled in the literature against the use of ARMA models for estimating long run properties is put into perspective. Methodological issues arising in the estimation of ARMA models that are relevant to estimation of persistence are discussed. It is shown how overparameterization of an ARMA model may lead to severely downward biased estimates of persistence. The theoretical results are employed to explain some of the findings in Campbell & Mankiw (1987a) and Christiano & Eichenbaum (1990). The methodological aspects of the paper are also relevant for the problem of estimating the value of a spectral density at any given frequency. An empirical study confirms persistence estimates reported in Campbell & Mankiw (1987a), and shows that ARMA models as well as nonparametric procedures give very similar estimates of persistence if properly applied.

Suggested Citation

  • Erhard Reschenhofer & Benedikt M. Pötscher & Michael A. Hauser, 1999. "Measuring persistence in aggregate output: ARMA models, fractionally integrated ARMA models and nonparametric procedures," Empirical Economics, Springer, vol. 24(2), pages 243-269.
    • Handle: RePEc:spr:empeco:v:24:y:1999:i:2:p:243-269
    Note: received: May 1996/final version received: March 1998
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    Cited by:

    1. Patrick Fève & Alain Guay, 2010. "Identification of Technology Shocks in Structural Vars," Economic Journal, Royal Economic Society, vol. 120(549), pages 1284-1318, December.
    2. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    3. Belbute, José, 2013. "Does final demand for energy in Portugal exhibit long memory?," MPRA Paper 45717, University Library of Munich, Germany.
    4. Aaron D. Smallwood & Stefan C. Norrbin, 2006. "Generalized long memory processes, failure of cointegration tests and exchange rate dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 409-417, May.
    5. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    6. María Dolores Gadea & Laura Mayoral, 2006. "The Persistence of Inflation in OECD Countries: A Fractionally Integrated Approach," International Journal of Central Banking, International Journal of Central Banking, vol. 2(1), March.
    7. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    8. 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.
    9. Hassler, Uwe & Hosseinkouchack, Mehdi, 2014. "Effect of the order of fractional integration on impulse responses," Economics Letters, Elsevier, vol. 125(2), pages 311-314.
    10. Ossama Mikhail & Curtis J. Eberwein & Jagdish Handa, 2003. "Testing and Estimating Persistence in Canadian Unemployment," Econometrics 0311004, University Library of Munich, Germany.
    11. Guay, Alain & Pelgrin, Florian, 2023. "Structural VAR models in the Frequency Domain," Journal of Econometrics, Elsevier, vol. 236(1).
    12. Hassler, Uwe, 2012. "Impulse responses of antipersistent processes," Economics Letters, Elsevier, vol. 116(3), pages 454-456.
    13. Paul Johnson & Chris Papageorgiou, 2020. "What Remains of Cross-Country Convergence?," Journal of Economic Literature, American Economic Association, vol. 58(1), pages 129-175, March.
    14. Chaker Aloui, 2003. "Long-Range Dependence in Daily Volatility on Tunisian Stock Market," Working Papers 0340, Economic Research Forum, revised Dec 2003.
    15. Stefan C. Norrbin & Aaron D. Smallwood, 2006. "Generalized long memory processes, failure of cointegration tests and exchange rate dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 409-417.
    16. Stefan Norrbin & Aaron Smallwood, 2010. "Generalized long memory and mean reversion of the real exchange rate," Applied Economics, Taylor & Francis Journals, vol. 42(11), pages 1377-1386.
    17. Yuliya Lovcha & Alejandro Perez-Laborda, 2017. "Structural shocks and dynamic elasticities in a long memory model of the US gasoline retail market," Empirical Economics, Springer, vol. 53(2), pages 405-422, September.
    18. Coleman, Simeon, 2010. "Inflation persistence in the Franc zone: Evidence from disaggregated prices," Journal of Macroeconomics, Elsevier, vol. 32(1), pages 426-442, March.
    19. Giorgio Canarella & Stephen M. Miller, 2016. "Inflation Targeting: New Evidence from Fractional Integration and Cointegration," Working papers 2016-08, University of Connecticut, Department of Economics.
    20. O. Mikhail & C. J. Eberwein & J. Handa, 2006. "Estimating persistence in Canadian unemployment: evidence from a Bayesian ARFIMA," Applied Economics, Taylor & Francis Journals, vol. 38(15), pages 1809-1819.
    21. Mercedes Alda & Luis Ferruz, 2012. "Linear and nonlinear financial time series: evidence in a sample of pension funds in Spain and the United Kingdom," Applied Economics Letters, Taylor & Francis Journals, vol. 19(18), pages 1933-1937, December.

    More about this item

    Keywords

    ARMA model · fractionally integrated ARMA model · persistence · spectral density estimation;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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