This paper proposes a test for assessing the accuracy of an assumed nonlinear regression model with long memory design and heteroscedastic long memory errors. The test is based on the marked empirical process. The asymptotic distributions of the proposed test statistics are investigated. The leave-one-observation-out kernel type estimator of the conditional variance function is also constructed in order to implement the lack of fit test.

中文翻译：

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缺乏长记忆回归模型的拟合测试

本文提出了一种测试，用于评估具有长记忆设计和异方差长记忆错误的假定非线性回归模型的准确性。该测试基于标记的经验过程。研究了所提出的检验统计量的渐近分布。还构造了条件方差函数的留一观察核类型估计器，以实现失拟检验。