IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/9505001.html
   My bibliography  Save this paper

Bayesian Analysis of Long Memory and Persistence using ARFIMA Models

Author

Listed:
  • Gary Koop

    (Dept of Economics, University of Leicester, UK)

  • Eduardo Ley

    (IMF, Washington DC, USA)

  • Jacek Osiewalski

    (Academy of Economics, Krakow, Poland)

  • Mark F.J. Steel

    (Dept of Statistics, University of Warwick, UK)

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 & Eduardo Ley & Jacek Osiewalski & Mark F.J. Steel, 1995. "Bayesian Analysis of Long Memory and Persistence using ARFIMA Models," Econometrics 9505001, EconWPA, revised 22 Jun 2004.
  • Handle: RePEc:wpa:wuwpem:9505001
    Note: PDF replaced to display the graphics correctly. Published in The Journal of Econometrics, 76:1-2 (January), pages 149-170, 1997.
    as

    Download full text from publisher

    File URL: http://econwpa.repec.org/eps/em/papers/9505/9505001.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    3. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    4. Diebold, Francis X & Rudebusch, Glenn D, 1991. "Is Consumption Too Smooth? Long Memory and the Deaton Paradox," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 1-9, February.
    5. 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.
    6. Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363.
    7. Tieslau, M.A. & Schmidt, P. & Baillie, R.T., 1992. "A Generalized Method of Moments Estimator for Long-Memory Processes," Papers 9100, Michigan State - Econometrics and Economic Theory.
    8. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    9. John Y. Campbell & N. Gregory Mankiw, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 857-880.
    10. Beveridge, Steve & Oickle, Cyril, 1993. "Estimating fractionally integrated time series models," Economics Letters, Elsevier, vol. 43(2), pages 137-142.
    11. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    12. Tieslau, M. & Schmidt, P. & Baillie, R., 1992. "A Generalized Method of Moments Estimator for Long-Memory Processes," Discussion Paper 1992-47, Tilburg University, Center for Economic Research.
    13. Koop, Gary & Osiewalski, Jacek & Steel, Mark F J, 1994. "Posterior Properties of Long-Run Impulse Responses," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 489-492, October.
    14. 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.
    15. Koop, Gary, 1991. "Intertemporal Properties of Real Output: A Bayesian Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 253-265, July.
    16. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
    17. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
    18. 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.
    19. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
    20. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
    21. Baillie, R.T. & Chung, C,F. & Tieslau, M.A., 1992. "The Long Memory and Variability of Inflation : A Reappraisal of the Friedman Hypothesis," Papers 9246, Tilburg - Center for Economic Research.
    22. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    23. Baillie, R. & Chung, C. & Tieslau, M., 1992. "The Long Memory and Variability of Inflation : A Reappraisal of the Friedman Hypothesis," Discussion Paper 1992-46, Tilburg University, Center for Economic Research.
    24. Granger, C. W. J. & Andersen, Allan, 1978. "On the invertibility of time series models," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 87-92, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    3. repec:exl:2manag:v:16:y:2015:i:1:p:7-37 is not listed on IDEAS
    4. 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.
    5. 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.
    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, Department of Economics, 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. Enrique Moral-Benito, 2010. "Model Averaging in Economics," Working Papers wp2010_1008, CEMFI.
    10. Steel, Mark F. J., 2017. "Model Averaging and its Use in Economics," MPRA Paper 81568, University Library of Munich, Germany.
    11. Ossama Mikhail & Curtis J. Eberwein & Jagdish Handa, 2003. "Testing and Estimating Persistence in Canadian Unemployment," Econometrics 0311004, EconWPA.
    12. Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
    13. Krzysztof Brania & Henryk Gurgul, 2015. "The impact of estimation methods and data frequency on the results of long memory assessment," Managerial Economics, AGH University of Science and Technology, vol. 16(1), pages 7-37, January.
    14. 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.
    15. 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.
    16. 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.
    17. Gonçalves Mazzeu, Joao Henrique & Ruiz, Esther & Veiga, Helena, 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.
    18. 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.
    19. 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.
    20. repec:rss:jnljfe:v1i1p3 is not listed on IDEAS
    21. 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.
    22. Enrique Moral-Benito, 2015. "Model Averaging In Economics: An Overview," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 46-75, February.

    More about this item

    Keywords

    Fractionally Integrated Models; Impulse Responses; Time Series; Trend Stationarity; Unit Root;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:9505001. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: http://econwpa.repec.org .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.