Long Memory and Hysteresis

  • Christian de Peretti

Summary

The aim of this chapter is to determine whether the hysteretic series can be confused with long memory series, since the hysteretic effect is a persistence in the series like the long memory effect.

Nevertheless, the long term behavior of the hysteretic series is very different from the long term behavior of the long memory series: the hysteretic series are not mean reverting whereas the long memory series are (if correctly differencied). Since the mean reverting property is crucial for many economic models for checking the stability of equilibria, distinguishing between hysteresis and long memory is very important. This difference is due to the fact that hysteresis models have in fact a short memory, since dominant shocks erase the memory of the series, and the persistence is due to permanent and nonreverting state changes at a microstructure level. For checking whether hysteretic series can display long memory property, a model possessing the hysteresis property is used for simulating hysteretic data. Statistical tests for short memory against long memory alternatives are applied to these simulated data.

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References

  1. 1.
    Amable, B., Henry, J., Lordon, F. and Topol, R. (1991). Strong Hysteresis: an Application to Foreign Trade. OFCE Working Paper, 91(3).Google Scholar
  2. 2.
    Amable, B., Henry, J., Lordon, F. and Topol, R. (1995). Hysteresis revisited: A methodological approach. In R. Cross (ed.), The Natural Rate of Unemployment: Reflections on 25 Years of the Hypothesis. Cambridge University Press, Cambridge.Google Scholar
  3. 3.
    Andersson, M. K. and Gredenhoff, M. P. (1998). Robust testing for fractional integration using the bootstrap. Working paper series in economics and finance, 218.Google Scholar
  4. 4.
    Arthur, W. B., Holland, J. H., LeBaron, B., Palmer, R. and Taylor, P. (1997). Asset pricing under endogenous expectations in an artificial stock market. In: Durlauf, S. N., Arthur, W. B., and Lane, D. A. (Eds.), The Economy as an Evolving Complex System II, 15–44. Reading, MA: Addison-Wesley.Google Scholar
  5. 5.
    Brock, W. A. (1993). Pathways to randomness in the economy: emergent nonlinearity and chaos in economics and finance. Estudios Económicos, 8, 3–55.Google Scholar
  6. 6.
    Brock, W. A. (1997). Asset price behavior in complex environments. In: Durlauf, S. N., Arthur, W. B., and Lane, D. A. (eds.), The Economy as an Evolving Complex System, Vol II, 385–423. Reading MA: Addison-Wesley.Google Scholar
  7. 7.
    Brock, W. A. and Hommes, C. H. (1997a). A rational route to randomness. Econometrica, 65, 1059–1095.MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Brock, W. A. and Hommes, C. H. (1997b). Models of complexity in economics and finance. In: C Hey et al (Eds.), System dynamics in economic and financial models, 3–41. New York: Wiley.Google Scholar
  9. 9.
    Brock, W. A. and Hommes, C. H. (1998). Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics Control, 22, 1235–1274.MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Brock, W. A. and Hommes, C. H. (1999). Rational animal spirits. In: Van der Laan, G., Herings, P. J. J., and Talman, A. J. J. (eds.) The Theory of Markets, 109–137. Amsterdam: North-Holland.Google Scholar
  11. 11.
    Brock, W. A. and LeBaron, B. (1996). A structural model for stock return volatility and trading volume. Review of Economic Statistics, 78, 94–110.CrossRefGoogle Scholar
  12. 12.
    Chiarella, C. (1992). The dynamics of speculative behaviour. Ann. Operations Research, 37, 101–123.MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Chiarella, C. and He, T. (2002). Heterogeneous beliefs, risk and learning in a simple asset pricing model. Computational Economics, 19, 95–132.MATHCrossRefGoogle Scholar
  14. 14.
    Coakley, J., Fuertes, A.M. and Zoega, G. (2002). Evaluating the persistence and structuralist theories of unemployment. Studies in Nonlinear Dynamics and Econometrics, 5, 1–22.Google Scholar
  15. 15.
    Cross, R. (1993). On the foundations of hysteresis in economic systems. Economics and Philosophy, 9, April, 53–74.CrossRefGoogle Scholar
  16. 16.
    Cross, R., Darby, J., Ireland, J. and Piscitelli, L. (1998). Hysteresis and unemployment: a preliminary investigation. CEPR/ESRC Unemployment Dynamics Workshop Paper, February.Google Scholar
  17. 17.
    Cross, R., Krasnosel’Skii, A. M. and Pokrovskii, A. V. (2001). A time-dependent Preisach model. Physica B, 306, 206–210.CrossRefADSGoogle Scholar
  18. 18.
    Cross, R., Piscitelli, L., Grinfeld, M. and Lamba, H. (2000). A test for strong hysteresis. Computational Economics, 15, 59–78.MATHCrossRefGoogle Scholar
  19. 19.
    Dacorogna, M. M., Müller, U. A., Jost, C., Pictet, O. V., Olsen, R. B. and Ward, J. R. (1995). Heterogeneous real-time trading strategies in the foreign exchange market. European Journal of Finance, 1, 383–403.CrossRefGoogle Scholar
  20. 20.
    Davidson, R. and MacKinnon, J. G. (1993). Estimation and inference in economics. Oxford University Press, New York.Google Scholar
  21. 21.
    Davidson, R. and MacKinnon, J. G. (1996). The power of bootstrap tests. Queen’s University Institute for Economic Research, Discussion Paper, 937.Google Scholar
  22. 22.
    Davidson, R. and MacKinnon, J. G. (1998). Graphical methods for investigating the size and the power of hypothesis tests. The Manchester School, 66, 1–22.CrossRefGoogle Scholar
  23. 23.
    Davidson, R. and MacKinnon, J. G. (1999). The size distortion of bootstrap tests. Econometric Theory, 15, 361–376.MATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    DeGrauwe, P., DeWachter, H. and Embrechts, M. (1993). Exchange Rate Theory, Chaotic Models of Foreign Exchange Markets. Oxford: Blackwell.Google Scholar
  25. 25.
    De Long, J. B., Shleifer, A., Summers, L. H. and Waldmann, R. J. (1990). Noise trader risk in financial markets. Journal of Political Economy, 98, 703–738.CrossRefGoogle Scholar
  26. 26.
    van Dijk, D. and Franses, P. H. and Paap, R. (2002). A nonlinear memory model for US unemployment. Journal of Econometrics, 110, 135–165.MATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    Dixit, A. (1989). Entry and exit decisions under uncertainty. Journal of Political Economy, 93,.Google Scholar
  28. 28.
    Dixit, A. and Pindyck, R. (1994). Investment Under Uncertainty. Princeton university press, Princeton.Google Scholar
  29. 29.
    Efron, B. (1979). Bootstrap methods: another look at the Jacknife. Annals of Statistics, 7, 1–26.MATHMathSciNetCrossRefGoogle Scholar
  30. 30.
    Fama, E. F. (1965). Random walks in stock market prices. Financial Analysts Journal, September/October (reprinted January–February 1995).Google Scholar
  31. 31.
    Farmer, J. D. (1998). Market force, ecology, and evolution. Santa Fe Institute Working Paper, 98-12-117.Google Scholar
  32. 32.
    Farmer, J. D. and Joshi, S. (2002). The price dynamics of common trading strategies. Journal of Economic Behaviour Organization, 49,.Google Scholar
  33. 33.
    Frankel, J. A. and Froot, K. A. (1988). Chartists, fundamentalists and the demand for dollars. Greek Economic Review, 10, 49–102.Google Scholar
  34. 34.
    Gaunersdorfer, A. (2000). Endogenous fluctuations in a simple asset pricing model with heterogeneous beliefs. Journal of Economic Dynamics and Control, 24, 799–831.MATHCrossRefGoogle Scholar
  35. 35.
    Gaunersdorfer, A. and Hommes, C. H. (2005). A nonlinear structural model for volatility clustering. In: Teyssiére, G. and Kirman, A. (Eds.), Long-Memory in Economics. Springer Verlag, Berlin. Appears in this volume.Google Scholar
  36. 36.
    Giraitis, L., Kokoszka, P., Leipus, R., and Teyssiére, G. (2003). Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics, 112, 265–294.MATHMathSciNetCrossRefGoogle Scholar
  37. 37.
    Göcke, M. (2002). Various concept of hysteresis applied in economics. Journal of Economic Surveys, 16, 167–188.CrossRefGoogle Scholar
  38. 38.
    Granger, C. W. J. and Joyeux, R. (1980). An introduction to long-memory time series models and fractional integration. Journal of Time Series Analysis, 1, 15–29.MATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    Hammermesh, D. (1989). Labour demand and the structure of qdjustment costs. American Economic Review, 79, 674–689.Google Scholar
  40. 40.
    Henry, M. and Robinson, P. M. (1996). Bandwidth choice in Gaussian semiparametric estimation of long range dependence. Athens Conference on Applied Probability and Time Series Analysis, II, Lecture Notes in Statistics, 115, Springer: New York.Google Scholar
  41. 41.
    Heyde, C. C. (2002). On modes of long range dependence. Journal of Applied Probability, 39, 882–888.MATHMathSciNetCrossRefGoogle Scholar
  42. 42.
    Higuchi, T. (1988). Approach to an irregular time series on the basis of the fractal theory. Physica, D 31, 277–283.MATHMathSciNetADSGoogle Scholar
  43. 43.
    Hosking, J. R. M. (1981). Fractional differencing. Biometrika, 68, 165–176.MATHMathSciNetCrossRefGoogle Scholar
  44. 44.
    Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transac. Am. Soc. Civil Eng., 116, 770–808.Google Scholar
  45. 45.
    Jensen, M. J. (1994). Wavelet analysis of fractionally integrated processes. Dep. of Economics, Washington University, St. Louis, MO 63130.Google Scholar
  46. 46.
    Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. Macmillan Press.Google Scholar
  47. 47.
    Kirman, A. P. (1991). Epidemics of opinion and speculative bubbles in financial markets. In Taylor, M. (ed), Money and Financial Markets, London: Macmillan.Google Scholar
  48. 48.
    Kirman, A. P. and Teyssiére, G. (2000). Microeconomic models for long-memory in the volatility of financial time series. Studies in Nonlinear Dynamics and Econometrics, 5, 281–302.CrossRefGoogle Scholar
  49. 49.
    Krasnosel’Skii, M. A. and Pokrovskii, A. W. (1989). Systems wich Hysteresis. Springer Verlag, Berlin.Google Scholar
  50. 50.
    Kurz, M. (1997). Endogenous Economic Fluctuations. Berlin: Springer.MATHGoogle Scholar
  51. 51.
    Layard, R., Nickell, S. and Jackman, R. (1991). Unemployment. Macroeconomic performance and the labour market. Oxford University Press.Google Scholar
  52. 52.
    Lang, D. and de Peretti, C. (2003). A strong hysteretic model for Okun’s law: Theory and preliminary investigation. Preprint.Google Scholar
  53. 53.
    LeBaron, B. (2000). Agent based computational finance: suggested readings and early research. Journal of Economic Dynamics and Control, 24, 679–702.MATHCrossRefGoogle Scholar
  54. 54.
    LeBaron, B., Arthur, W. B. and Palmer, R. (1999). Time series properties of an artificial stock market. Journal of Economic Dynamics and Control, 23, 1487–1516.MATHCrossRefGoogle Scholar
  55. 55.
    Lo, A. W. (1991). Long-term memory in stock market price. Econometrica, 59, 1279–1313.MATHMathSciNetCrossRefGoogle Scholar
  56. 56.
    Lux, T. (1995). Herd behavior, bubbles and crashes. The Economic Journal, 105, 881–896.CrossRefGoogle Scholar
  57. 57.
    Lux, T. and Marchesi, M., (1999). Scaling and criticality in a stochatic multiagent model of a financial market. Nature, 397, 498–500.CrossRefADSGoogle Scholar
  58. 58.
    Lux, T. and Marchesi, M. (2000). Volatility clustering in financial markets: a micro-simulation of interactive agents. International Journal of Theoretical Applied Finance, 3, 675–702.MATHMathSciNetCrossRefGoogle Scholar
  59. 59.
    Marshall, A. (1890). Principles of Economics, 1st edition. Macmillan, London.Google Scholar
  60. 60.
    Mayergoyz, (1991). Mathematical Models of Hysteresis. Springer Verlag, Berlin.MATHCrossRefGoogle Scholar
  61. 61.
    Oi, W. (1962). Labour as a quasi-fixed factor. Journal of Political Economy, 70, 538–555.CrossRefGoogle Scholar
  62. 62.
    de Peretti, C. (2003a). Bilateral bootstrap tests for long memory: an application to the silver market. Computational Economics, 22, 187–212.MATHCrossRefGoogle Scholar
  63. 63.
    de Peretti, C. (2003b). Graphical methods for investigating the finite-sample properties of confidence regions: Application to the long memory parameter. Preprint.Google Scholar
  64. 64.
    de Peretti, C. and Marimoutoo, V. (2002). Are the long memory tests really effective? Preprint.Google Scholar
  65. 65.
    Robinson, P. M. (1995). Gaussian semiparametric estimation of long range dependence. The Annals of Statistics, 23, 1048–1072.MATHMathSciNetCrossRefGoogle Scholar
  66. 66.
    Wang, J. (1994). A model of competitive stock trading volume. Journal of political Economy, 102, 127–168.CrossRefGoogle Scholar
  67. 67.
    Zeeman, E. C. (1974). The unstable behavior of stock exchange. Journal of Mathematical Economics, 1 39–49.MATHMathSciNetCrossRefGoogle Scholar
  68. 68.
    Zoega, G., Booth, A. L., and Chen, Y.-F (2002). Hiring and firing: a tale of two thresholds. Journal of Labour Economics, 20, 217–248.CrossRefGoogle Scholar

Copyright information

© Springer Berlin · Heidelberg 2007

Authors and Affiliations

  • Christian de Peretti
    • 1
  1. 1.Department of Economics, Finance, and International BusinessLondon Metropolitan UniversityLondon

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