Testing of a sub-hypothesis in linear regression models with long memory errors and deterministic design

This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models where errors form long memory moving average processes and designs are non-random. Unlike in the random design case, asymptotic null distribution of the likelihood ratio type test based on the Whittle quadratic form is shown to be non-standard an() non-chi-square. Moreover, the rate of consistency of the minimum Whittle dispersion estimator of the slope parameter vector is shown to be n(-(1-alpha)/2), different from the rate n(-1/2) obtained in the random design case, where alpha is the rate at which the error spectral density explodes at the origin. The proposed test is shown to be consistent against fixed alternatives and has non-trivial asymptotic power against local alternatives that converge to null hypothesis at the rate n(-(1-alpha)/2). (C) 2008 Elsevier B.V. All rights reserved.