We propose a two-step procedure to detect cointegration in high-dimensional settings, focusing on sparse relationships. First, we use the adaptive LASSO to identify the small subset of integrated covariates driving the equilibrium relationship with a target series, ensuring model-selection consistency. Second, we adopt an information-theoretic model choice criterion to distinguish between stationarity and nonstationarity in the resulting residuals, avoiding dependence on asymptotic distributional assumptions. Monte Carlo experiments confirm robust finite-sample performance, even under endogeneity and serial correlation.

翻译：本文提出一种两阶段方法，用于高维场景下的协整关系检测，重点关注稀疏关联结构。第一阶段采用自适应LASSO算法识别与目标序列存在均衡关系的少数积分型协变量，确保模型选择的一致性。第二阶段基于信息论模型选择准则，对所得残差序列的平稳性与非平稳性进行判别，避免对渐近分布假设的依赖。蒙特卡洛实验表明，该方法在内生性与序列相关性存在的情况下仍具有稳健的有限样本性能。