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Statistical Papers

, Volume 45, Issue 4, pp 465–515 | Cite as

Long memory versus structural breaks: An overview

  • Philipp Sibbertsen
Survey Article

Abstract

We discuss the increasing literature on misspecifying structural breaks or more general trends as long-range dependence. We consider tests on structural breaks in the long-memory regression model as well as the behaviour of estimators of the memory parameter when structural breaks or trends are in the data but long memory is not. Methods for distinguishing both of these phenomena are proposed.

Key words

Long memory structural breaks trends 

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References

  1. Abry P., Veitch, D. (1998): “Wavelet Analysis of Long-Range-Dependent Traffic.”IEEE Transactions on Information Theory 44, 2–15.MATHCrossRefMathSciNetGoogle Scholar
  2. Andrews, D. W. K., Ploberger, W. (1994): “Optimal tests when a nuisance parameter is present only under the alternative.”Econometrica 62, 1383–1414.MATHCrossRefMathSciNetGoogle Scholar
  3. Bai, J. (1994): “Least squares estimation of a shift in linear processes.”Journal of Time Series Analysis 15, 453–472.MATHMathSciNetGoogle Scholar
  4. Beran, J. (1994):Statistics for long-memory processes. Chapman & Hall, New York.MATHGoogle Scholar
  5. Beran, J. (1995): “Maximum likelihood estimation of the differencing parameter for invertible short- and long-memory ARIMA models.”Journal of the Royal Statistical Society B 57, No. 4,, 659–672.MATHMathSciNetGoogle Scholar
  6. Beran, J., Feng, Y. (1999): “Local polynomial fitting with long-memory errors.”Working paper, University of Konstanz.Google Scholar
  7. Beran, J., Feng, Y., Ocker, D. (1998): “SEMIFAR models”Working paper, University of Konstanz.Google Scholar
  8. Beran, J., Ghosh, S., Sibbertsen, P. (2002a): “Nonparametric M-estimation with long-memory errors.”Journal of Statistical Planning and Inference, forthcoming.Google Scholar
  9. Beran, J., Feng, Y., Ghosh, S., Sibbertsen, P. (2002b): “On robust local polynomial estimation with long-memory errors.”International Journal of Forecasting 18, 227–241.CrossRefGoogle Scholar
  10. Bhattacharya, R. N., Gupta, V. K., Waymire, E. (1983): “The Hurst Effect under Trends.”Journal of Applied Probability 20, 649–662.MATHCrossRefMathSciNetGoogle Scholar
  11. Bollerslev, T., Mikkelsen, H. O. (1996): “Modeling and pricing long memory in stock market volatility.”Journal of Econometrics 73, 151–184.MATHCrossRefMathSciNetGoogle Scholar
  12. Brown, R. L., Durbin, J. andEvans, J. M. (1975): “Techniques for testing the constancy of regression relationships over time.”Journal of the Royal Statistical Society B 37, 149–163.MATHMathSciNetGoogle Scholar
  13. Cheung, Y. (1993): “Long Memory in Foreign-Exchange Rates.”Journal of Business and Economics Statistics 11, 93–101.CrossRefGoogle Scholar
  14. Csörgö, S., Mielniczuk, J. (1995): “Nonparametric regression under long-range dependent normal errors.”Annals of Statistics 23, 1000–1014.MATHMathSciNetGoogle Scholar
  15. Dahlhaus, R. (1989): “Efficient parameter estimation for self-similar processes.”The Annals of Statistics 17, 1749–1766.MATHMathSciNetGoogle Scholar
  16. Davidson, J. (2000): “When is a time series I(0)? Evaluating the Memory Properties of Nonlinear Dynamic Models.”Working Paper, Cardiff Business School.Google Scholar
  17. Davidson, J., De Jong, R. (2000): “The functional central limit theorem and weak convergence to stochastic integrals II.”Econometric Theory 16, 643–666.MATHCrossRefMathSciNetGoogle Scholar
  18. De Jong, R., Davidson, J. (2000): “The functional central limit theorem and weak convergence to stochastic integrals I”Econometric Theory 16, 621–642.MATHCrossRefMathSciNetGoogle Scholar
  19. Diebold, F. X., Inoue, A. (2001): “Long memory and Regime Switching.”Journal of Econometrics 105, 131–159.MATHCrossRefMathSciNetGoogle Scholar
  20. Engle, R. F. (1982): “Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation.”Econometrica 50, 987–1008.MATHCrossRefMathSciNetGoogle Scholar
  21. Fan, J., Gijbels, I. (1996):Local polynomial modeling and its applications. Chapman & Hall, London.Google Scholar
  22. Geweke, J., Porter-Hudak, S. (1983): “The estimation and application of long-memory time series models.”Journal of Time Series Analysis 4, 221–237.MATHMathSciNetGoogle Scholar
  23. Giraitis, L., Kokoszka, P., Leipus, R. (2001): “Testing for long memory in the presence of a general trend.”Journal of Applied Probability 38, 1033–1054.MATHCrossRefMathSciNetGoogle Scholar
  24. Giraitis, L., Kokoszka, P., Leipus, R., Teysierre, G. (2002): “Rescaled variance and related tests for long memory in volatilities and levels.”Journal of Econometrics, forthcoming.Google Scholar
  25. Gourieroux, C., Jasiak, J. (2001): “Memory and infrequent breaks.”Economics Letters 70, 29–41.MATHCrossRefMathSciNetGoogle Scholar
  26. Granger, C. W. J. (1966): “The typical spectral shape of an economic variable.”Econometrica 34, 150–161.CrossRefGoogle Scholar
  27. Granger, C. W. J., Joyeux, R. (1980): “An introduction to long-range time series models and fractional differencing.”Journal of Time Series Analysis 1, 15–30.MATHMathSciNetGoogle Scholar
  28. Granger, C. W. J., Hyung, N. (1999): “Occasional structural breaks and long memory.”Discussion paper 99-14, University of California, SatSan Diego.Google Scholar
  29. Hall, P., Hart, J. (1990): “Nonparametric regression with long-range dependence.”Stochastic Processes and their Applications 36, 339–351.MATHCrossRefMathSciNetGoogle Scholar
  30. Hidalgo, J. andRobinson, P.M. (1996): “Testing for structural change in a long-memory environment.”Journal of Econometrics 70, 159–174.MATHCrossRefMathSciNetGoogle Scholar
  31. Horvath, L., Kokoszka, P. (1997): “The effect of long-range dependence on change-point estimators”.Journal of Statistical Planning and Inference 64, 57–81.MATHCrossRefMathSciNetGoogle Scholar
  32. Hosking, J. R. M. (1981): “Fractional differencing”.Biometrika 68, 165–176.MATHCrossRefMathSciNetGoogle Scholar
  33. Hurvich, C., Deo, R. andBrodsky, J. (1998): “The Mean Squared Error of Geweke and Porter-Hudak's estimator of the Memory Parameter of a Long-Memory Time Series”.Journal of Time Series Analysis 19, 19–46.MATHCrossRefMathSciNetGoogle Scholar
  34. Jensen, M. J. (1999): “Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long-memory Parameter”.Journal of Forecasting 18, 17–32.CrossRefGoogle Scholar
  35. Krämer, W., Sibbertsen, P. (2003): “Testing for structural change in the presence of long memory”.International Journal of Business and Economics 1, 235–243.Google Scholar
  36. Künsch, H. R. (1986): “Discrimination between monotonic trends and long-range dependence”.Journal of Applied Probability 23, 1025–1030.MATHCrossRefMathSciNetGoogle Scholar
  37. Lohre, M., Sibbertsen, P. (2002): “Persistenz und saisonale Abhängigkeiten in Abflüssen des Rheins”.Hydrology and Water Resources Management 46, 166–174.Google Scholar
  38. Mandelbrot, B. B. (1975): “Limit theorems on the selfnormalized range for weakly and strongly dependent processes”.Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 31, 271–285.MATHCrossRefMathSciNetGoogle Scholar
  39. Mandelbrot, B. B., van Ness, J. W. (1968): “Fractional Brownian motions, fractional noises and applications”.SIAM Review 10, 422–437.MATHCrossRefMathSciNetGoogle Scholar
  40. Mandelbrot, B. B., Wallis, J. R. (1969): Some long-run properties of geophysical records.Water resources research 5, 321–340.CrossRefGoogle Scholar
  41. Ploberger, W. andKrämer, W. (1992): “The CUSUM-test with OLS-residuals”.Econometrica 60, 271–286.MATHCrossRefMathSciNetGoogle Scholar
  42. Robinson, P. (1995): “Log-periodogram regression of time series with long-range dependence”.Annals of Statistics 23, 1048–1072.MATHMathSciNetGoogle Scholar
  43. Sibbertsen, P. (2002): “Log-periodogram estimation of the memory parameter of a long-memory process under trend”.Statistics and Probability Letters, forthcoming.Google Scholar
  44. Stock, J. H. (1994): “Unit roots and trend breaks”. In R. F. Engle and D. Mc Fadden (eds)Handbook of Econometrics, Volume IV, North-Holland, Amsterdam.Google Scholar
  45. Taqqu, M.S. (1975): “Weak convergence of fractional Brownian Motion to the Rosenblatt process”.Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 31, 287–302.MATHCrossRefMathSciNetGoogle Scholar
  46. Teverovsky, V., Taqqu, M. (1997): “Testing for long-range dependence in the presence of shifting means or a slowly declining trend using a variance-type estimator”.Journal of Time Series Analysis 18, 279–304.MATHCrossRefMathSciNetGoogle Scholar
  47. Velasco, C. (1999): “Non-Stationary Log-Periodogram Regression”.Journal of Econometrics 91, 325–371.MATHCrossRefMathSciNetGoogle Scholar
  48. Yajima, Y. (1985): “On estimation of long-memory time series models”.Australian Journal of Statistics 27, 303–320.MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Philipp Sibbertsen
    • 1
  1. 1.Fachbereich StatistikUniversität DortmundDortmundGermany

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