Simultaneous inference of a partially linear model in time series
提出一种新方法，用于对部分线性时间序列回归模型中的非参数部分进行联合推断，构建多元函数的联合置信区域，适用于多种线性和非线性自回归过程，并在远期溢价回归中验证了有效性。
We introduce a new methodology to conduct simultaneous inference of the non‐parametric component in partially linear time series regression models where the non‐parametric part is a multi‐variate unknown function. In particular, we construct a simultaneous confidence region (SCR) for the multi‐variate 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 non‐linear 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.