Abstract
This paper discusses some tests of lack-of-fit of a parametric regression model when errors form a long memory moving average process with the long memory parameter \(0<d<1/2\), and when design is non-random and uniform on \([0,1]\). These tests are based on certain minimized distances between a nonparametric regression function estimator and the parametric model being fitted. The paper investigates the asymptotic null distribution of the proposed test statistics and of the corresponding minimum distance estimators under minimal conditions on the model being fitted. The limiting distribution of these statistics are Gaussian for \(0<d<1/4\) and non-Gaussian for \(1/4<d<1/2\). We also discuss the consistency of these tests against a fixed alternative. A simulation study is included to assess the finite sample behavior of the proposed test.
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Authors wish to thank the two anonymous referees for thoughtful comments that helped to improve the presentation.
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H. L. Koul Research supported in part by NSF DMS Grant 1205271. D. Surgailis thanks the Michigan State University for hosting his visit from April 7 to May 10, 2013, during which this work was completed. Research of D. Surgailis was also supported in part by Grant MIP- 063/2013 from the Research Council of Lithuania.
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Koul, H.L., Surgailis, D. & Mimoto, N. Minimum distance lack-of-fit tests under long memory errors. Metrika 78, 119–143 (2015). https://doi.org/10.1007/s00184-014-0492-x
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DOI: https://doi.org/10.1007/s00184-014-0492-x