This paper proposes a novel canonical correlation analysis for semiparametric inference in $I(1)/I(0)$ systems via functional approximation. The approach can be applied coherently to panels of $p$ variables with a generic number $s$ of stochastic trends, as well as to subsets or aggregations of variables. This study discusses inferential tools on $s$ and on the loading matrix $\psi$ of the stochastic trends (and on their duals $r$ and $\beta$, the cointegration rank and the cointegrating matrix): asymptotically pivotal test sequences and consistent estimators of $s$ and $r$, $T$-consistent, mixed Gaussian and efficient estimators of $\psi$ and $\beta$, Wald tests thereof, and misspecification tests for checking model assumptions. Monte Carlo simulations show that these tools have reliable performance uniformly in $s$ for small, medium and large-dimensional systems, with $p$ ranging from 10 to 300. An empirical analysis of 20 exchange rates illustrates the methods.

翻译：本文提出了一种新颖的典型相关分析方法，通过函数逼近实现$I(1)/I(0)$系统中的半参数推断。该方法可一致地应用于包含$p$个变量且具有任意数量$s$个随机趋势的面板数据，以及变量的子集或聚合数据。本研究讨论了关于$s$和随机趋势载荷矩阵$\psi$（及其对偶量$r$与$\beta$，即协整秩与协整矩阵）的推断工具：关于$s$和$r$的渐近枢轴检验序列与一致估计量，关于$\psi$和$\beta$的$T$一致、混合高斯且有效的估计量，相应的Wald检验，以及用于检验模型假设的误设定检验。蒙特卡洛模拟表明，这些工具在$p$从10到300的小型、中型及大型维度系统中，对任意$s$均具有可靠的性能表现。对20种汇率的实证分析展示了该方法的应用。