Canonical correlation analysis of stochastic trends via functional approximation
提出一种半参数推断方法，结合函数逼近和典型相关分析，估计I(1)/I(0)系统中共同趋势的数量及载荷矩阵，并给出相关检验。蒙特卡洛模拟显示有限样本表现合理，并用20种汇率数据做了实证。研究经济时间序列共同趋势的学者可参考。
This paper proposes a novel approach for semiparametric inference on the number s of common trends and their loading matrix ψ in I(1)/I(0) systems. It combines functional approximation of limits of random walks and canonical correlation analysis, performed between the p observed time series of length T and the first K discretized elements of an L2 basis. Tests and selection criteria for s and estimators and tests on ψ are proposed; their properties are discussed as T and K diverge sequentially for fixed p and s. It is found that tests on s are asymptotically pivotal, selection criteria of s are consistent, estimators of ψ are T-consistent, mixed-Gaussian and efficient, so that Wald tests on ψ are asymptotically normal or χ2. The paper also discusses asymptotically pivotal misspecification tests for checking model assumptions. The approach can be coherently applied to subsets or aggregations of variables in a given panel. Monte Carlo simulations show that these tools have reasonable performance for T≥10p and p≤300. An empirical analysis of 20 exchange rates illustrates the methods.