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SPECTRAL DENSITY ESTIMATION AND ROBUST HYPOTHESIS TESTING USING STEEP ORIGIN KERNELS WITHOUT TRUNCATION *
Author(s) -
Phillips Peter C. B.,
Sun Yixiao,
Jin Sainan
Publication year - 2006
Publication title -
international economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.658
H-Index - 86
eISSN - 1468-2354
pISSN - 0020-6598
DOI - 10.1111/j.1468-2354.2006.00398.x
Subject(s) - mathematics , estimator , asymptotic distribution , truncation (statistics) , monte carlo method , exponent , sample size determination , statistics , test statistic , spectral density , limit (mathematics) , delta method , statistical hypothesis testing , statistical physics , mathematical analysis , physics , philosophy , linguistics
A new class of kernels for long‐run variance and spectral density estimation is developed by exponentiating traditional quadratic kernels. Depending on whether the exponent parameter is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimators. When the exponent is passed to infinity with the sample size, the new estimator is consistent and shown to be asymptotically normal. When the exponent is fixed, the new estimator is inconsistent and has a nonstandard limiting distribution. It is shown via Monte Carlo experiments that, when the chosen exponent is small in practical applications, the nonstandard limit theory provides better approximations to the finite sample distributions of the spectral density estimator and the associated test statistic in regression settings.