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Learning generates Long Memory

  • Guillaume Chevillon

    (ESSEC Business School - ESSEC Business School)

  • Sophocles Mavroeidis

    (University of Oxford - Department of Economics)

We consider a prototypical representative-agent forward-looking model, and study the low frequency variability of the data when the agent's beliefs about the model are updated through linear learning algorithms. We find that learning in this context can generate strong persistence. The degree of persistence depends on the weights agents place on past observations when they update their beliefs, and on the magnitude of the feedback from expectations to the endogenous variable. When the learning algorithm is recursive least squares, long memory arises when the coefficient on expectations is sufficiently large. In algorithms with discounting, long memory provides a very good approximation to the low-frequency variability of the data. Hence long memory arises endogenously, due to the self-referential nature of the model, without any persistence in the exogenous shocks. This is distinctly different from the case of rational expectations, where the memory of the endogenous variable is determined exogenously. Finally, this property of learning is used to shed light on some well-known empirical puzzles.

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Date of creation: Oct 2013
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Handle: RePEc:hal:journl:hal-00661012
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  1. Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
  2. Francis X. Diebold & Glenn D. Rudebusch, 1990. "On the power of Dickey-Fuller tests against fractional alternatives," Finance and Economics Discussion Series 119, Board of Governors of the Federal Reserve System (U.S.).
  3. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
  4. John Y. Campbell & Motohiro Yogo, 2002. "Efficient Tests of Stock Return Predictability," Harvard Institute of Economic Research Working Papers 1972, Harvard - Institute of Economic Research.
  5. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
  6. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
  7. Delgado, Miguel A. & Robinson, Peter M., 1996. "Optimal spectral kernel for long-range dependent time series," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 37-43, September.
  8. Wiliam Branch & George W. Evans, . "Asset Return Dynamics and Learning," University of Oregon Economics Department Working Papers 2006-14, University of Oregon Economics Department.
  9. Fama, Eugene F., 1984. "Forward and spot exchange rates," Journal of Monetary Economics, Elsevier, vol. 14(3), pages 319-338, November.
  10. Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
  11. Baillie, Richard T. & Bollerslev, Tim, 2000. "The forward premium anomaly is not as bad as you think," Journal of International Money and Finance, Elsevier, vol. 19(4), pages 471-488, August.
  12. Jes�s Gonzalo & Jean-Yves Pitarakis, 2006. "Threshold Effects in Cointegrating Relationships," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 813-833, December.
  13. Davidson, James & Sibbertsen, Philipp, 2002. "Generating schemes for long memory processes: Regimes, aggregation and linearity," Technical Reports 2002,46, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  14. Davidson, James & Hashimzade, Nigar, 2008. "Alternative Frequency And Time Domain Versions Of Fractional Brownian Motion," Econometric Theory, Cambridge University Press, vol. 24(01), pages 256-293, February.
  15. Offer Lieberman & Peter C.B. Phillips, 2006. "A Complete Asymptotic Series for the Autocovariance Function of a Long Memory Process," Cowles Foundation Discussion Papers 1586, Cowles Foundation for Research in Economics, Yale University.
  16. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October.
  17. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695, March.
  18. Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
  19. Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-45, June.
  20. Jeffrey A. Frankel & Kenneth A. Froot, 1985. "Using Survey Data to Test Some Standard Propositions Regarding Exchange Rate Expectations," NBER Working Papers 1672, National Bureau of Economic Research, Inc.
  21. Clarida, R. & Gali, J. & Gertler, M., 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Working Papers 99-13, C.V. Starr Center for Applied Economics, New York University.
  22. Peter C.B. Phillips, 1999. "Unit Root Log Periodogram Regression," Cowles Foundation Discussion Papers 1244, Cowles Foundation for Research in Economics, Yale University.
  23. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
  24. Ulrich Mueller & Mark W. Watson, 2006. "Testing Models of Low-Frequency Variability," NBER Working Papers 12671, National Bureau of Economic Research, Inc.
  25. D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
  26. Shiller, Robert J, 1989. " Comovements in Stock Prices and Comovements in Dividends," Journal of Finance, American Finance Association, vol. 44(3), pages 719-29, July.
  27. 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.
  28. Davidson, James & Terasvirta, Timo, 2002. "Long memory and nonlinear time series," Journal of Econometrics, Elsevier, vol. 110(2), pages 105-112, October.
  29. Marcus J. Chambers, . "Long Memory and Aggregation in Macroeconomic Time Series," Economics Discussion Papers 437, University of Essex, Department of Economics.
  30. Frankel, Jeff & Froot, Ken, 1986. "Using Survey Data to Test Standard Propositions Regarding Exchange Rate Expectations," Department of Economics, Working Paper Series qt1972q8wm, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  31. Gourieroux, C & Laffont, J J & Monfort, Alain, 1982. "Rational Expectations in Dynamic Linear Models: Analysis of the Solutions," Econometrica, Econometric Society, vol. 50(2), pages 409-25, March.
  32. Karim Abadir & Gabriel Talmain, . "Aggregation, Persistence and Volatility in a Macromodel," Discussion Papers 01/03, Department of Economics, University of York.
  33. Baillie, Richard T & Bollerslev, Tim, 1994. "The long memory of the forward premium," Journal of International Money and Finance, Elsevier, vol. 13(5), pages 565-571, October.
  34. L Giraitis & P C B Phillips, . "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
  35. Fabio Milani, 2005. "Expectations, Learning and Macroeconomic Persistence," Macroeconomics 0510022, EconWPA.
  36. Chevillon, Guillaume & Massmann, Michael & Mavroeidis, Sophocles, 2010. "Inference in models with adaptive learning," Journal of Monetary Economics, Elsevier, vol. 57(3), pages 341-351, April.
  37. Ulrike Malmendier & Stefan Nagel, 2009. "Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking?," NBER Working Papers 14813, National Bureau of Economic Research, Inc.
  38. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  39. Joon Y. Park & J. Isaac Miller, 2004. "Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory," Econometric Society 2004 North American Summer Meetings 597, Econometric Society.
  40. Donald W. K. Andrews & Patrik Guggenberger, 2008. "Asymptotics for stationary very nearly unit root processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 203-212, 01.
  41. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series /2001/420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  42. Peter C.B. Phillips & Tassos Magdalinos & Liudas Giraitis, 2008. "Smoothing Local-to-Moderate Unit Root Theory," Cowles Foundation Discussion Papers 1659, Cowles Foundation for Research in Economics, Yale University.
  43. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
  44. Alex Maynard & Peter C. B. Phillips, 2001. "Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 671-708.
  45. 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.
  46. George W. Evans & Avik Chakraborty, 2006. "Can Perpetual Learning Explain the Forward Premium Puzzle?," University of Oregon Economics Department Working Papers 2006-8, University of Oregon Economics Department, revised 20 Aug 2006.
  47. 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.
  48. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
  49. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
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