Acta Applicandae Mathematica

, Volume 78, Issue 1–3, pp 285–299 | Cite as

On the Power of R/S-Type Tests under Contiguous and Semi-Long Memory Alternatives

  • Liudas Giraitis
  • Piotr Kokoszka
  • Remigijus Leipus
  • Gilles Teyssière


The paper deals with the power and robustness of the R/S type tests under “contiguous” alternatives. We briefly review some long memory models in levels and volatility, and describe the R/S-type tests used to test for the presence of long memory. The empirical power of the tests is investigated when replacing the fractional difference operator (1−L) d by the operator (1−rL) d , with r<1 close to 1, in the FARIMA, LARCH and ARCH time series models. We also investigate the Gegenbauer process with a pole of the spectral density at frequency close to zero.

long memory Gegenbauer process ARCH processes linear ARCH semi-long memory modified R/S statistic KPSS statistic V/S statistic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Andel, J.: Long memory time series models, Kybernetica 22(1986), 105–123.Google Scholar
  2. 2.
    Baillie, R. T., Bollerslev, T. and Mikkelsen, H. O.: Fractionally integrated generalized autoregressive conditional heteroskedasticity, J. Econometrics 74(1996), 3–30.Google Scholar
  3. 3.
    Beran, J.: Statistics for Long-Memory Processes, Chapman and Hall, London, 1994.Google Scholar
  4. 4.
    Davidson, R. and MacKinnon, J. G.: Graphical methods for investigating the size and power of hypothesis tests, The Manchester School 66(1998), 1–26.Google Scholar
  5. 5.
    Den Haan, W. J. and Levin, A.: A practitioner's guide to robust covariance matrix estimation, In:G.S. Maddala and C.R. Rao (eds),Handbook of Statistics, Vol. 15, 1997, pp. 291–341.Google Scholar
  6. 6.
    Ding, Z. and Granger, C. W. J.: Modeling volatility persistence of speculative returns: a new approach, J. Econometrics 73(1996), 185–215.Google Scholar
  7. 7.
    Giraitis, L., Hidalgo, J. and Robinson, P. M.: Gaussian estimation of parametric spectral density with unknown pole, Ann. Statist. 29(2001), 987–1023.Google Scholar
  8. 8.
    Giraitis, L., Kokoszka, P. S. and Leipus, R.: Stationary ARCH models: Dependence structure and central limit theorem, Econometric Theory 16(2000), 3–22.Google Scholar
  9. 9.
    Giraitis, L., Kokoszka, P. S., Leipus, R. and Teyssiére, G.: Rescaled variance and related tests for long memory in volatility and levels, J. Econometrics 112(2003), 265–294.Google Scholar
  10. 10.
    Giraitis, L., Robinson, P. M. and Surgailis, D.: A model for long memory conditional heteroskedasticity, Ann. Appl. Probab. 10(2000), 1002–1024.Google Scholar
  11. 11.
    Giraitis, L. and Surgailis, D.: ARCH-type bilinear models with double long memory, Stochast. Processes Appl. 100(2002), 275–300.Google Scholar
  12. 12.
    Granger, C. W. J. and Joyeux, R.: An introduction to long-memory time series models and fractional differencing, J. Time Ser. Anal. 1(1980), 15–29.Google Scholar
  13. 13.
    Gray, H. L., Zhang, N. F. and Woodward, W. A.: On generalized fractional processes, J. Time Ser. Anal. 10(1989), 233–257.Google Scholar
  14. 14.
    Hosking, J. R. M.: Fractional differencing, Biometrika 68(1981), 165–176.Google Scholar
  15. 15.
    Hurst, H. E.: Long-term storage capacity of reservoirs, Trans. Amer. Soc. Civil Eng. 116(1951), 770–799.Google Scholar
  16. 16.
    Kazakevičius, V. and Leipus, R.: A new theorem on existence of invariant distributions with applications to ARCH processes, J. Appl. Probab. 40(2003), 147–162.Google Scholar
  17. 17.
    Kwiatkowski, D., Phillips, P. C. B., Schmidt, P. and Shin, Y.: Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic series have a unit root? J. Econometrics 54(1992), 159–178.Google Scholar
  18. 18.
    Lee, D. and Schmidt, P.: On the power of the KPSS test of stationarity against fractionally-integrated alternatives, J. Econometrics 73(1996), 285–302.Google Scholar
  19. 19.
    Lo, A. W.: Long-term memory in stock market prices, Econometrica 59(1991), 1279–1313.Google Scholar
  20. 20.
    Newey, W. K. and West, K. D.: A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica 55(1987), 703–708.Google Scholar
  21. 21.
    Robinson, P. M.: Testing for strong serial correlation and dynamic conditional heteroskedastic-ity in multiple regression, J. Econometrics 47(1991), 67–84.Google Scholar
  22. 22.
    Robinson, P. M.: Time series with strong dependence, In: C. A. Sims (ed.), Advances in Econometrics, Sixth World Congress, Cambridge Univ. Press, 1994, pp. 47–95.Google Scholar
  23. 23.
    Teyssiére, G.: Nonlinear and semi-parametric long-memory ARCH, Preprint.Google Scholar
  24. 24.
    Vogelsang, T. J.: Sources of nonmonotonic power when testing for a shift in mean of a dynamic time series, J. Econometrics 88(1999), 283–299.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Liudas Giraitis
  • Piotr Kokoszka
  • Remigijus Leipus
  • Gilles Teyssière

There are no affiliations available

Personalised recommendations