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Consistent And Conservative Model Selection With The Adaptive Lasso In Stationary And Nonstationary Autoregressions

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  • Kock, Anders Bredahl

Abstract

We show that the adaptive Lasso is oracle efficient in stationary and nonstationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency as if only these had been included in the model from the outset. In particular, this implies that it is able to discriminate between stationary and nonstationary autoregressions and it thereby constitutes an addition to the set of unit root tests. Next, and important in practice, we show that choosing the tuning parameter by Bayesian Information Criterion (BIC) results in consistent model selection. However, it is also shown that the adaptive Lasso has no power against shrinking alternatives of the form c/T if it is tuned to perform consistent model selection. We show that if the adaptive Lasso is tuned to perform conservative model selection it has power even against shrinking alternatives of this form and compare it to the plain Lasso.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:01:p:243-259_00
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    Cited by:

    1. Thilo Reinschlussel & Martin C. Arnold, 2024. "Information-Enriched Selection of Stationary and Non-Stationary Autoregressions using the Adaptive Lasso," Papers 2402.16580, arXiv.org, revised Jul 2024.
    2. Matteo Barigozzi & Christian Brownlees, 2019. "NETS: Network estimation for time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 347-364, April.
    3. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    4. Fan, Rui & Lee, Ji Hyung & Shin, Youngki, 2023. "Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach," Journal of Econometrics, Elsevier, vol. 237(2).
    5. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    6. Koo, Bonsoo & Anderson, Heather M. & Seo, Myung Hwan & Yao, Wenying, 2020. "High-dimensional predictive regression in the presence of cointegration," Journal of Econometrics, Elsevier, vol. 219(2), pages 456-477.
    7. Tu, Yundong & Xie, Xinling, 2023. "Penetrating sporadic return predictability," Journal of Econometrics, Elsevier, vol. 237(1).
    8. 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.
    9. Laurent Callot & Johannes Tang Kristensen, 2014. "Vector Autoregressions with Parsimoniously Time Varying Parameters and an Application to Monetary Policy," CREATES Research Papers 2014-41, Department of Economics and Business Economics, Aarhus University.
    10. Efstathios Polyzos & Costas Siriopoulos, 2024. "Autoregressive Random Forests: Machine Learning and Lag Selection for Financial Research," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 225-262, July.
    11. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    12. Karsten Schweikert, 2022. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 83-104, January.
    13. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    14. Julien Hambuckers & Li Sun & Luca Trapin, 2023. "Measuring tail risk at high-frequency: An $L_1$-regularized extreme value regression approach with unit-root predictors," Papers 2301.01362, arXiv.org.
    15. Alessi, Lucia & Balduzzi, Pierluigi & Savona, Roberto, 2019. "Anatomy of a Sovereign Debt Crisis: CDS Spreads and Real-Time Macroeconomic Data," JRC Working Papers in Economics and Finance 2019-03, Joint Research Centre, European Commission.
    16. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    17. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    18. Mr. Jorge A Chan-Lau, 2017. "Lasso Regressions and Forecasting Models in Applied Stress Testing," IMF Working Papers 2017/108, International Monetary Fund.
    19. Caraiani, Petre, 2022. "Using LASSO-family models to estimate the impact of monetary policy on corporate investments," Economics Letters, Elsevier, vol. 210(C).
    20. Chor-yiu Sin & Shu-Hui Yu, 2019. "Order selection for possibly infinite-order non-stationary time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 187-216, June.
    21. David Neto, 2023. "Penalized leads-and-lags cointegrating regression: a simulation study and two empirical applications," Empirical Economics, Springer, vol. 65(2), pages 949-971, August.

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