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Bayesian Analysis of Long Memory and Persistence using ARFIMA Models

  • Gary Koop

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.

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File URL: https://www.economics.utoronto.ca/public/workingPapers/UT-ECIPA-GKOOP-95-01.ps
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Paper provided by University of Toronto, Department of Economics in its series Working Papers with number gkoop-95-01.

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Length: 25 pages
Date of creation: 24 May 1995
Date of revision:
Handle: RePEc:tor:tecipa:gkoop-95-01
Contact details of provider: Postal: 150 St. George Street, Toronto, Ontario
Phone: (416) 978-5283

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  1. 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 103-12, January.
  2. Yin-Wong Cheung & Francis X. Diebold, 1990. "On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean," Discussion Paper / Institute for Empirical Macroeconomics 34, Federal Reserve Bank of Minneapolis.
  3. 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.
  4. Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis.
  5. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
  12. 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.
  13. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  14. 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.
  15. Min, C.K. & Zellner, A., 1992. ""Bayesian and Non-Bayesian Methods for Combining Models and Forecasts with Applications to Forecasting International Growth Rates"," Papers 90-92-23, California Irvine - School of Social Sciences.
  16. Koop, Gary, 1991. "Intertemporal Properties of Real Output: A Bayesian Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 253-65, July.
  17. John Y. Campbell & N. Gregory Mankiw, 1986. "Are Output Fluctuations Transitory?," NBER Working Papers 1916, National Bureau of Economic Research, Inc.
  18. 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.
  19. 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.
  20. Beveridge, Steve & Oickle, Cyril, 1993. "Estimating fractionally integrated time series models," Economics Letters, Elsevier, vol. 43(2), pages 137-142.
  21. 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 489-92, October.
  22. 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.
  23. 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.
  24. 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.
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