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Detecting Sparse Cointegration

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  • Gonzalo, Jesús
  • Pitarakis, Jean-Yves

Abstract

We propose a two-step procedure for detecting sparse cointegration in high-dimensional singleequation models. First, we employ the adaptive lasso to identify the subset of integrated covariates driving the long-run equilibrium relationship. Second, we adopt an information-theoretic criterion to distinguish between stationarity and nonstationarity in the resulting residuals, avoiding reliance on asymptotic distributions. A key theoretical contribution is demonstrating that this residualbased decision rule remains consistent regardless of the internal cointegration structure among the right-hand side predictors themselves. Monte Carlo experiments confirm the procedure'srobust finite-sample performance under endogeneity, serial correlation, and rank deficiency in the regressor matrix.

Suggested Citation

  • Gonzalo, Jesús & Pitarakis, Jean-Yves, 2026. "Detecting Sparse Cointegration," UC3M Working papers. Economics 49894, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:49894
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    References listed on IDEAS

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    1. Kock, Anders Bredahl, 2016. "Consistent And Conservative Model Selection With The Adaptive Lasso In Stationary And Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 32(1), pages 243-259, February.
    2. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    3. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    4. Alexei Onatski & Chen Wang, 2018. "Alternative Asymptotics for Cointegration Tests in Large VARs," Econometrica, Econometric Society, vol. 86(4), pages 1465-1478, July.
    5. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(1), pages 91-115, March.
    6. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
    7. Xiao, Zhijie & Phillips, Peter C. B., 2002. "A CUSUM test for cointegration using regression residuals," Journal of Econometrics, Elsevier, vol. 108(1), pages 43-61, May.
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    2. Karsten Reichold & Ulrike Schneider, 2025. "Beyond the Oracle Property: Adaptive LASSO in Cointegrating Regressions with Local-to-Unity Regressors," Papers 2510.07204, arXiv.org, revised Mar 2026.

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    Keywords

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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