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Detecting sparse cointegration

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  • Gonzalo, Jesús
  • Pitarakis, Jean-Yves

Abstract

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.

Suggested Citation

  • Gonzalo, Jesús & Pitarakis, Jean-Yves, 2025. "Detecting sparse cointegration," UC3M Working papers. Economics 45708, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:45708
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    References listed on IDEAS

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    1. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    2. 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.
    3. 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.
    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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    Cited by:

    1. 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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