This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for I(1) linear processes, using canonical correlation analysis and functional approximation of Brownian Motions. It proposes inference criteria based on the estimation of the number of common trends in various subsets of variables, and compares them to sequences of tests of hypotheses. The exact limit distribution for one of the test statistics is derived in the univariate case. Properties of the inferential tools are discussed theoretically and illustrated via a Monte Carlo study. An empirical analysis of exchange rates is also included.

翻译：本文利用典型相关分析和布朗运动的函数逼近方法，讨论了I(1)线性过程的协整与吸引子空间假设的半参数推断。研究提出了基于变量不同子集中共同趋势数量估计的推断准则，并将其与假设检验序列进行比较。在单变量情形下，推导了其中一个检验统计量的精确极限分布。通过理论分析和蒙特卡洛模拟研究，探讨了推断工具的性质。文中还包含了对汇率数据的实证分析。