IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Learning generates Long Memory

  • Guillaume Chevillon

    (ESSEC Business School - Essec Business School)

  • Sophocles Mavroeidis

    (University of Oxford (UK) - University of Oxford [Oxford])

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: https://hal-essec.archives-ouvertes.fr/hal-00661012v2/document
Download Restriction: no

Paper provided by HAL in its series Post-Print with number hal-00661012.

as
in new window

Length:
Date of creation: Oct 2013
Date of revision:
Publication status: Published in ESSEC Working paper. Document de recherche de l'ESSEC / ISSN : 1291-9616 WP1113 Updated October 2013. 2013, pp.49
Handle: RePEc:hal:journl:hal-00661012
Note: View the original document on HAL open archive server: https://hal-essec.archives-ouvertes.fr/hal-00661012v2
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Baillie, R.T. & Bollerslev, T., 1993. "Cointegration, Fractional Cointegration, and Exchange RAte Dynamics," Papers 9103, Michigan State - Econometrics and Economic Theory.
  2. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. 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.
  4. Chambers, Marcus J, 1995. "Long Memory and Aggregation in Macroeconomic Time Series," Economics Discussion Papers 2766, University of Essex, Department of Economics.
  5. 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.
  6. 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.
  7. Charles Engel & Kenneth D. West, 2003. "Exchange rates and fundamentals," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  8. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
  9. 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.
  10. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
  11. 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.
  12. Francis X. Diebold & Atsushi Inoue, 2000. "Long Memory and Regime Switching," NBER Technical Working Papers 0264, National Bureau of Economic Research, Inc.
  13. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
  14. Sargent, Thomas J., 1993. "Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198288695, June.
  15. 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.
  16. Gonzalo, J. & Pitarakis, J., 2005. "Threshold effects in cointegrating relationships," Discussion Paper Series In Economics And Econometrics 0506, Economics Division, School of Social Sciences, University of Southampton.
  17. Baillie, R.T. & Bollerslev, T., 1993. "The Long Memory of the Foreward Premium," Papers 9203, Michigan State - Econometrics and Economic Theory.
  18. Wiliam Branch & George W. Evans, . "Asset Return Dynamics and Learning," University of Oregon Economics Department Working Papers 2006-14, University of Oregon Economics Department.
  19. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  20. Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, vol. 155(1), pages 83-89, March.
  21. Karim Abadir & Gabriel Talmain, 2001. "Aggregation, Persistence and Volatility in a Macromodel," Working Papers w200106, Banco de Portugal, Economics and Research Department.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. L Giraitis & P C B Phillips, . "Uniform limit theory for stationary autoregression," Discussion Papers 05/23, Department of Economics, University of York.
  27. Milani, Fabio, 2007. "Expectations, learning and macroeconomic persistence," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2065-2082, 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. Lieberman, Offer & Phillips, Peter C.B., 2008. "A complete asymptotic series for the autocovariance function of a long memory process," Journal of Econometrics, Elsevier, vol. 147(1), pages 99-103, November.
  30. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
  31. 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.
  32. 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.
  33. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
  34. 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.
  35. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  36. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, 09.
  37. 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.
  38. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February.
  39. Lo, Andrew W. (Andrew Wen-Chuan), 1989. "Long-term memory in stock market prices," Working papers 3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  40. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
  41. 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.
  42. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
  43. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
  44. Ulrike Malmendier & Stefan Nagel, 2009. "Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking?," NBER Working Papers 14813, National Bureau of Economic Research, Inc.
  45. Davidson, James & Sibbertsen, Philipp, 2005. "Generating schemes for long memory processes: regimes, aggregation and linearity," Journal of Econometrics, Elsevier, vol. 128(2), pages 253-282, October.
  46. Fama, Eugene F., 1984. "Forward and spot exchange rates," Journal of Monetary Economics, Elsevier, vol. 14(3), pages 319-338, November.
  47. 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.
  48. Phillips, Peter C.B. & Magdalinos, Tassos & Giraitis, Liudas, 2010. "Smoothing local-to-moderate unit root theory," Journal of Econometrics, Elsevier, vol. 158(2), pages 274-279, October.
  49. 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.
  50. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00661012. 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: (CCSD)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.