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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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