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Subset selection for vector autoregressive processes via adaptive Lasso

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  • Ren, Yunwen
  • Zhang, Xinsheng

Abstract

Subset selection is a critical component of vector autoregressive (VAR) modeling. This paper proposes simple and hybrid subset selection procedures for VAR models via the adaptive Lasso. By a proper choice of tuning parameters, one can identify the correct subset and obtain the asymptotic normality of the nonzero parameters with probability tending to one. Simulation results show that for small samples, a particular hybrid procedure has the best performance in terms of prediction mean squared errors, estimation errors and subset selection accuracy under various settings. The proposed method is also applied to modeling the IS-LM data for illustration.

Suggested Citation

  • Ren, Yunwen & Zhang, Xinsheng, 2010. "Subset selection for vector autoregressive processes via adaptive Lasso," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1705-1712, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1705-1712
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    References listed on IDEAS

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    Citations

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    1. Ziel, Florian, 2016. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR–ARCH type processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 773-793.
    2. Florian Ziel & Rick Steinert & Sven Husmann, 2014. "Efficient Modeling and Forecasting of the Electricity Spot Price," Papers 1402.7027, arXiv.org, revised Oct 2014.
    3. Daniel Ambach & Robert Garthoff, 2016. "Vorhersagen der Windgeschwindigkeit und Windenergie in Deutschland," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(1), pages 15-36, February.
    4. Camehl, Annika, 2023. "Penalized estimation of panel vector autoregressive models: A panel LASSO approach," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1185-1204.
    5. Schnücker, A.M., 2019. "Penalized Estimation of Panel Vector Autoregressive Models," Econometric Institute Research Papers EI-2019-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Florian Ziel, 2015. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes," Papers 1502.06557, arXiv.org, revised Dec 2015.
    7. 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.
    8. Daniel Ambach & Carsten Croonenbroeck, 2016. "Space-time short- to medium-term wind speed forecasting," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 5-20, March.
    9. Ziel, Florian & Steinert, Rick & Husmann, Sven, 2015. "Efficient modeling and forecasting of electricity spot prices," Energy Economics, Elsevier, vol. 47(C), pages 98-111.
    10. Daniel Ambach & Robert Garthoff, 2016. "Vorhersagen der Windgeschwindigkeit und Windenergie in Deutschland [Predictions of wind speed and wind energy in Germany]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(1), pages 15-36, February.
    11. Ren, Yunwen & Xiao, Zhiguo & Zhang, Xinsheng, 2013. "Two-step adaptive model selection for vector autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 349-364.
    12. Daniel Ambach & Carsten Croonenbroeck, 2016. "Space-time short- to medium-term wind speed forecasting," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 5-20, March.
    13. Mihai C. Giurcanu, 2017. "Oracle M-Estimation for Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(3), pages 479-504, May.
    14. 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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