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An Automated Approach Towards Sparse Single-Equation Cointegration Modelling

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  • Stephan Smeekes
  • Etienne Wijler

Abstract

In this paper we propose the Single-equation Penalized Error Correction Selector (SPECS) as an automated estimation procedure for dynamic single-equation models with a large number of potentially (co)integrated variables. By extending the classical single-equation error correction model, SPECS enables the researcher to model large cointegrated datasets without necessitating any form of pre-testing for the order of integration or cointegrating rank. Under an asymptotic regime in which both the number of parameters and time series observations jointly diverge to infinity, we show that SPECS is able to consistently estimate an appropriate linear combination of the cointegrating vectors that may occur in the underlying DGP. In addition, SPECS is shown to enable the correct recovery of sparsity patterns in the parameter space and to posses the same limiting distribution as the OLS oracle procedure. A simulation study shows strong selective capabilities, as well as superior predictive performance in the context of nowcasting compared to high-dimensional models that ignore cointegration. An empirical application to nowcasting Dutch unemployment rates using Google Trends confirms the strong practical performance of our procedure.

Suggested Citation

  • Stephan Smeekes & Etienne Wijler, 2018. "An Automated Approach Towards Sparse Single-Equation Cointegration Modelling," Papers 1809.08889, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1809.08889
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    Cited by:

    1. Marie Levakova & Susanne Ditlevsen, 2024. "Penalisation Methods in Fitting High‐Dimensional Cointegrated Vector Autoregressive Models: A Review," International Statistical Review, International Statistical Institute, vol. 92(2), pages 160-193, August.
    2. Simionescu, Mihaela & Cifuentes-Faura, Javier, 2022. "Can unemployment forecasts based on Google Trends help government design better policies? An investigation based on Spain and Portugal," Journal of Policy Modeling, Elsevier, vol. 44(1), pages 1-21.
    3. Jesus Gonzalo & Jean-Yves Pitarakis, 2025. "Detecting Sparse Cointegration," Papers 2501.13839, arXiv.org.
    4. Yao Li & Yugang He, 2024. "Unraveling Korea’s Energy Challenge: The Consequences of Carbon Dioxide Emissions and Energy Use on Economic Sustainability," Sustainability, MDPI, vol. 16(5), pages 1-29, March.
    5. Mei, Ziwei & Shi, Zhentao, 2024. "On LASSO for high dimensional predictive regression," Journal of Econometrics, Elsevier, vol. 242(2).
    6. Zhan Gao & Ji Hyung Lee & Ziwei Mei & Zhentao Shi, 2024. "LASSO Inference for High Dimensional Predictive Regressions," Papers 2409.10030, arXiv.org, revised Jan 2026.
    7. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Inference in Non-stationary High-Dimensional VARs," Papers 2302.01434, arXiv.org, revised Sep 2023.
    8. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.
    9. Zhang, Anan & Zheng, Yadi & Huang, Huang & Ding, Ning & Zhang, Chengqian, 2022. "Co-integration theory-based cluster time-varying load optimization control model of regional integrated energy system," Energy, Elsevier, vol. 260(C).
    10. Alina Stundziene & Vaida Pilinkiene & Jurgita Bruneckiene & Andrius Grybauskas & Mantas Lukauskas & Irena Pekarskiene, 2024. "Future directions in nowcasting economic activity: A systematic literature review," Journal of Economic Surveys, Wiley Blackwell, vol. 38(4), pages 1199-1233, September.
    11. Etienne Wijler, 2022. "A restricted eigenvalue condition for unit-root non-stationary data," Papers 2208.12990, arXiv.org.
    12. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    13. Karsten Reichold & Ulrike Schneider, 2025. "Beyond the Oracle Property: Adaptive LASSO in Cointegrating Regressions," Papers 2510.07204, arXiv.org.

    More about this item

    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
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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