We introduce a new methodology to conduct simultaneous inference of the nonparametric component in partially linear time series regression models where the nonparametric part is a multivariate unknown function. In particular, we construct a simultaneous confidence region (SCR) for the multivariate function by extending the high-dimensional Gaussian approximation to dependent processes with continuous index sets. Our results allow for a more general dependence structure compared to previous works and are widely applicable to a variety of linear and nonlinear autoregressive processes. We demonstrate the validity of our proposed methodology by examining the finite-sample performance in the simulation study. Finally, an application in time series, the forward premium regression, is presented, where we construct the SCR for the foreign exchange risk premium from the exchange rate and macroeconomic data.

翻译：我们提出了一种新方法，用于对部分线性时间序列回归模型中的非参数成分进行联合推断，其中非参数部分是一个多元未知函数。具体而言，通过将高维高斯逼近推广至具有连续指标集的相依过程，我们为多元函数构建了联合置信区域（SCR）。与以往研究相比，我们的结果允许更一般的相依结构，并广泛适用于多种线性和非线性自回归过程。通过模拟研究检验有限样本性能，我们验证了所提方法的有效性。最后，我们展示了时间序列中的一个应用——远期升水回归，即利用汇率和宏观经济数据为外汇风险溢价构建联合置信区域。