Detecting Sparse Cointegration

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.

💡 Research Summary

The paper tackles the problem of detecting cointegration when a large number of candidate I(1) series are available but only a few of them actually participate in a long‑run equilibrium relationship with a target variable. This “sparse cointegration” setting is increasingly common in modern macro‑financial applications, yet traditional cointegration tools such as the Engle‑Granger two‑step method or Johansen’s maximum‑likelihood approach become infeasible because (i) the dimensionality of the regressor space explodes, (ii) ordinary least squares becomes unstable, and (iii) unit‑root tests rely on non‑standard limiting distributions that depend on the number of regressors.

The authors propose a simple two‑step procedure. In the first step they estimate the single‑equation cointegrating regression

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