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Nonparametric cointegrating regression models have been extensively used infinancial markets, stock prices, heavy traffic, climate data sets, and energymarkets. Models with parametric regression functions can be more appealing inpractice compared to non-parametric forms, but do result in potentialfunctional misspecification. Thus, there exists a vast literature on developinga model specification test for parametric forms of regression functions. Inthis paper, we develop two test statistics which are applicable for theendogenous regressors driven by long memory and semi-long memory input shocksin the regression model. The limit distributions of the test statistics underthese two scenarios are complicated and cannot be effectively used in practice.To overcome this difficulty, we use the subsampling method and compute the teststatistics on smaller blocks of the data to construct their empiricaldistributions. Throughout, Monte Carlo simulation studies are used toillustrate the properties of test statistics. We also provide an empiricalexample of relating gross domestic product to total output of carbon dioxide intwo European countries.

Properties of Test Statistics for Nonparametric Cointegrating Regression Functions Based on Subsamples