Nonparametric cointegrating regression models have been extensively used in financial markets, stock prices, heavy traffic, climate data sets, and energy markets. Models with parametric regression functions can be more appealing in practice compared to non-parametric forms, but do result in potential functional misspecification. Thus, there exists a vast literature on developing a model specification test for parametric forms of regression functions. In this paper, we develop two test statistics which are applicable for the endogenous regressors driven by long memory and semi-long memory input shocks in the regression model. The limit distributions of the test statistics under these two scenarios are complicated and cannot be effectively used in practice. To overcome this difficulty, we use the subsampling method and compute the test statistics on smaller blocks of the data to construct their empirical distributions. Throughout, Monte Carlo simulation studies are used to illustrate the properties of test statistics. We also provide an empirical example of relating gross domestic product to total output of carbon dioxide in two European countries.

翻译：非参数协整回归模型已广泛应用于金融市场、股票价格、高流量数据、气候数据集和能源市场。与半参数形式相比，参数回归函数模型在实践中更具吸引力，但可能导致函数设定的潜在错误。因此，已有大量文献致力于发展参数回归函数形式的模型设定检验。本文提出了两种检验统计量，适用于回归模型中由长记忆和半长记忆输入冲击驱动的内生回归元。这两种情形下检验统计量的极限分布复杂，无法在实际中有效使用。为克服这一困难，我们采用子抽样方法，在数据的较小块上计算检验统计量，以构建其经验分布。通过蒙特卡洛模拟研究，本文验证了检验统计量的性质。我们还提供了一个实证案例，将两个欧洲国家的国内生产总值与二氧化碳总产出相关联。