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Adaptative LASSO estimation for ARDL models with GARCH innovations

Author

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  • Marcelo C. Medeiros

    (Department of Economics PUC-Rio)

  • Eduardo F. Mendes

    (Department of Economics Australian School of Business)

Abstract

In this paper we show the validity of the adaptive LASSO procedure in estimating stationary ARDL(p,q) models with GARCH innovations. We show that, given a set of initial weights, the adaptive Lasso selects the relevant variables with probability converging to one. Afterwards, we show that the estimator is oracle, meaning that its distribution converges to the same distribution of the oracle assisted least squares, i.e., the least squares estimator calculated as if we knew the set of relevant variables beforehand. Finally, we show that the LASSO estimator can be used to construct the initial weights. The performance of the method in finite samples is illustrated using Monte Carlo simulation

Suggested Citation

  • Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "Adaptative LASSO estimation for ARDL models with GARCH innovations," Textos para discussão 637, Department of Economics PUC-Rio (Brazil).
    • Handle: RePEc:rio:texdis:637
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. Hsu, Nan-Jung & Hung, Hung-Lin & Chang, Ya-Mei, 2008. "Subset selection for vector autoregressive processes using Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3645-3657, March.
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    4. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    5. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    6. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    7. Zhang, Yiyun & Li, Runze & Tsai, Chih-Ling, 2010. "Regularization Parameter Selections via Generalized Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 312-323.
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    Cited by:

    1. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    2. 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.
    3. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2022. "Regularized estimation of high‐dimensional vector autoregressions with weakly dependent innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 532-557, July.

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