This article studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such models occur in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent or filtered variable as in mixed-data-sampling. The treatment allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable, including correctly specified as well as misspecified systems, and is therefore intermediate between nonlinear nonparametric cointegrating regression and completely spurious nonparametric nonstationary regression. The results relate to recent work on dynamic misspecification in nonparametric nonstationary systems and the limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series. Some implications for forecasting under misspecification are also examined.

中文翻译：

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潜变量非参数协整回归

本文研究了部分错误指定非平稳变量之间关系的经验非参数回归的渐近特性。特别是，我们分析了非参数核回归，其中潜在的非线性协整回归通过使用代理回归器代替真实回归器而被错误指定。此类模型出现在线性和非线性回归中，其中回归量存在测量误差，或者真正的回归量是混合数据采样中的潜在或过滤变量。该处理允许内生回归变量作为潜在变量和代理变量，它们与真实的潜在变量渐近协整，包括正确指定和错误指定的系统，因此介于非线性非参数协整回归和完全虚假的非参数非平稳回归之间。结果与最近关于非参数非平稳系统中动态错误指定的工作有关，极限理论适用于具有自回归根的回归变量，这些自回归根是局部于单位的，其误差由长记忆和短记忆创新驱动，因此涵盖了具有广泛经济价值的应用和金融时间序列。还研究了在错误规范下进行预测的一些影响。结果与最近关于非参数非平稳系统中动态错误指定的工作有关，极限理论适用于具有自回归根的回归变量，这些自回归根是局部于单位的，其误差由长记忆和短记忆创新驱动，因此涵盖了具有广泛经济价值的应用和金融时间序列。还研究了在错误规范下进行预测的一些影响。结果与最近关于非参数非平稳系统中动态错误指定的工作有关，极限理论适用于具有自回归根的回归变量，这些自回归根是局部于单位的，其误差由长记忆和短记忆创新驱动，因此涵盖了具有广泛经济价值的应用和金融时间序列。还研究了在错误规范下进行预测的一些影响。