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moving averages; linear regression; Whittle quadratic forms; chi-square
This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be $n^{1/2}$-consistent for all values of the long memory parameters of the design and error processes.
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