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Bayesian Analysis of Long Memory and Persistence using ARFIMA Models

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  • Gary Koop

Abstract

This paper provides a Bayesian analysis of Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. We discuss in detail inference on impulse responses, and show how Bayesian methods can be used to (i) test ARFIMA models against ARIMA alternatives, and (ii) take model uncertainty into account when making inferences on quantities of interest. Our methods are then used to investigate the persistence properties of real U.S. GNP.

Suggested Citation

  • Gary Koop, 1995. "Bayesian Analysis of Long Memory and Persistence using ARFIMA Models," Working Papers gkoop-95-01, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:gkoop-95-01
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    Cited by:

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    2. Yang Fuyu & Leon-Gonzalez Roberto, 2010. "Bayesian Estimation and Model Selection in the Generalized Stochastic Unit Root Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-38, September.
    3. Jacek Osiewalski & Justyna Wróblewska & Kamil Makieła, 2020. "Bayesian comparison of production function-based and time-series GDP models," Empirical Economics, Springer, vol. 58(3), pages 1355-1380, March.
    4. N. H. Chan & A. E. Brockwell, 2006. "Long-memory dynamic Tobit models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 351-367.
    5. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    6. Fuyu Yang, 2007. "Bayesian Analysis of Deterministic Time Trend and Changes in Persistence Using a Generalised Stochastic Unit Root Model," Discussion Papers in Economics 07/11, Division of Economics, School of Business, University of Leicester.
    7. 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.
    8. M. Dolores Gadea & Laura Mayoral, 2009. "Aggregation is not the solution: the PPP puzzle strikes back," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 875-894.
    9. Ossama Mikhail & Curtis J. Eberwein & Jagdish Handa, 2003. "Testing and Estimating Persistence in Canadian Unemployment," Econometrics 0311004, University Library of Munich, Germany.
    10. Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
    11. Epaminondas Panas & Vassilia Ninni, 2010. "The Distribution of London Metal Exchange Prices: A Test of the Fractal Market Hypothesis," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 192-210.
    12. Manveer Kaur Mangat & Erhard Reschenhofer, 2019. "Testing for Long-Range Dependence in Financial Time Series," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 11(2), pages 93-106, June.
    13. 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.
    14. Martin, Vance L. & Wilkins, Nigel P., 1999. "Indirect estimation of ARFIMA and VARFIMA models," Journal of Econometrics, Elsevier, vol. 93(1), pages 149-175, November.
    15. Andersson, Fredrik N. G. & Li, Yushu, 2014. "Are Central Bankers Inflation Nutters? - A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model," Discussion Papers 2014/38, Norwegian School of Economics, Department of Business and Management Science.
    16. Andersson, Fredrik N.G. & Li, Yushu, 2013. "How Flexible are the Inflation Targets? A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model," Working Papers 2013:38, Lund University, Department of Economics.
    17. Panas, E., 2001. "Long memory and chaotic models of prices on the London Metal Exchange," Resources Policy, Elsevier, vol. 27(4), pages 235-246, December.
    18. Micha³ Majsterek, 2018. "Stock and Flows in the Countegration Context," Lodz Economics Working Papers 3/2018, University of Lodz, Faculty of Economics and Sociology.
    19. Iglesias, Pilar & Jorquera, Hector & Palma, Wilfredo, 2006. "Data analysis using regression models with missing observations and long-memory: an application study," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2028-2043, April.
    20. Enrique Moral-Benito, 2010. "Model Averaging in Economics," Working Papers wp2010_1008, CEMFI.
    21. Ross Doppelt & Keith O'Hara, 2018. "Bayesian Estimation of Fractionally Integrated Vector Autoregressions and an Application to Identified Technology Shocks," 2018 Meeting Papers 1212, Society for Economic Dynamics.
    22. Veiga, Helena & Ruiz, Esther & Gonçalves Mazzeu, Joao Henrique, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    23. 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.
    24. Mohsen Mehrara & Nafiseh Behradmehr & Mitra Saboonchi, 2013. "Investigating the Long time Memory in the Future Market of Gold," International Journal of Financial Economics, Research Academy of Social Sciences, vol. 1(1), pages 28-32.
    25. Enrique Moral-Benito, 2015. "Model Averaging In Economics: An Overview," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 46-75, February.

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    More about this item

    Keywords

    Fractionally Integrated Models; Impulse Responses; Time Series; Trend Stationarity; Unit Root;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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