TY - JOUR
T1 - Local asymptotic powers of nonparametric and semiparametric tests for fractional integration
AU - Shao, Xiaofeng
AU - Wu, Wei Biao
N1 - Funding Information:
We would like to thank the editor and a referee for helpful comments. We are also grateful to Michael Stein for his constructive suggestions. The work is supported in part by NSF grant DMS-0478704.
PY - 2007/2
Y1 - 2007/2
N2 - The paper concerns testing long memory for fractionally integrated nonlinear processes. We show that the exact local asymptotic power is of order O [(log n)- 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 nκ, κ ∈ (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.
AB - The paper concerns testing long memory for fractionally integrated nonlinear processes. We show that the exact local asymptotic power is of order O [(log n)- 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 nκ, κ ∈ (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.
KW - Fractional integration
KW - KPSS test
KW - Lagrange multiplier test
KW - Local Whittle estimation
KW - Long memory
KW - R/S test
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U2 - 10.1016/j.spa.2006.08.002
DO - 10.1016/j.spa.2006.08.002
M3 - Article
AN - SCOPUS:33947190452
SN - 0304-4149
VL - 117
SP - 251
EP - 261
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -