Inference on the Attractor Space via Functional Approximation
研究线性过程中协整和吸引子空间的半参数推断方法，基于样本典型相关和布朗运动的函数逼近，适用于整个系统或线性组合，通过选择准则或检验序列进行推断，并给出极限分布和渐近性质，蒙特卡洛模拟和汇率实证验证了方法。
ABSTRACT This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for linear processes with moderately large cross‐sectional dimension. The approach is based on sample canonical correlations and functional approximation of Brownian motions, and it can be applied both to the whole system and or to any set of linear combinations of it. The hypotheses of interest are cast in terms of the number of stochastic trends in specified subsystems, and inference is based either on selection criteria or on sequences of tests. This paper derives the limit distribution of these tests in the special one‐dimensional case, and discusses asymptotic properties of the derived inference criteria for hypotheses on the attractor space for sequentially diverging sample size and number of basis elements in the functional approximation. Finite sample properties are analysed via a Monte Carlo study and an empirical illustration on exchange rates is provided.