Testing of a sub-hypothesis in linear regression models with long memory errors and deterministic design |
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Authors: | Hira L Koul Donatas Surgailis |
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Institution: | Michigan State University, Vilnius Institute of Mathematics and Informatics, USA |
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Abstract: | 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 and 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-α)/2, different from the rate n-1/2 obtained in the random design case, where α 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-α)/2. |
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Keywords: | primary 62M09 secondary 62M10 62M99 |
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