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Local asymptotic powers of nonparametric and semiparametric tests for fractional integration

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  • Shao, Xiaofeng
  • Wu, Wei Biao

Abstract

The paper concerns testing long memory for fractionally integrated nonlinear processes. We show that the exact local asymptotic power is of order O[(logn)-1] for four popular nonparametric tests and is O(m-1/2), where m is the bandwidth which is allowed to grow as fast as n[kappa], [kappa][set membership, variant](0,2/3), for the semiparametric Lagrange multiplier (LM) test proposed by Lobato and Robinson [I. Lobato, P.M. Robinson, A nonparametric test for I(0), Rev. Econom. Stud. 68 (1998) 475-495]. Our theory provides a theoretical justification for the empirical findings in finite sample simulations by Lobato and Robinson [I. Lobato, P.M. Robinson, A nonparametric test for I(0), Rev. Econom. Stud. 68 (1998) 475-495] and Giraitis et al. [L. Giraitis, P. Kokoszka, R. Leipus, G. Teyssiére, Rescaled variance and related tests for long memory in volatility and levels, J. Econometrics 112 (2003) 265-294] that nonparametric tests have lower power than LM tests in detecting long memory.

Suggested Citation

  • Shao, Xiaofeng & Wu, Wei Biao, 2007. "Local asymptotic powers of nonparametric and semiparametric tests for fractional integration," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 251-261, February.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:2:p:251-261
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    References listed on IDEAS

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    1. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus & Teyssiere, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," Journal of Econometrics, Elsevier, vol. 112(2), pages 265-294, February.
    2. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
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    6. Lee, Dongin & Schmidt, Peter, 1996. "On the power of the KPSS test of stationarity against fractionally-integrated alternatives," Journal of Econometrics, Elsevier, vol. 73(1), pages 285-302, July.
    7. Zhijie Xiao, 2001. "Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 87-105, January.
    8. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    9. Wright, Jonathan H., 1999. "The Local Asymptotic Power Of Certain Tests For Fractional Integration," Econometric Theory, Cambridge University Press, vol. 15(5), pages 704-709, October.
    10. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    11. Hurvich, Clifford M. & Soulier, Philippe, 2002. "Testing For Long Memory In Volatility," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1291-1308, December.
    12. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 475-495.
    13. GIRAITIS, Liudas & KOKOSZKA, Piotr & LEIPUS, Remigijus & TEYSSIÈRE, Gilles, 2003. "Rescaled variance and related tests for long memory in volatility and levels," LIDAM Reprints CORE 1594, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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