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Modified LASSO estimators for time series regression models with dependent disturbances

Author

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  • Yujie Xue

    (Waseda University)

  • Masanobu Taniguchi

    (Waseda University)

Abstract

This paper applies the modified least absolute shrinkage and selection operator (LASSO) to the regression model with dependent disturbances, especially, long-memory disturbances. Assuming the norm of different column in the regression matrix may have different order of observation length n, we introduce a modified LASSO estimator where the tuning parameter $$\lambda$$ λ is not a scalar but vector. When the dimension of parameters is fixed, we derive the asymptotic distribution of the modified LASSO estimators under certain regularity condition. When the dimension of parameters increases with respect to n, the consistency on the probability of the correct selection of penalty parameters is shown under certain regularity conditions. Some simulation studies are examined.

Suggested Citation

  • Yujie Xue & Masanobu Taniguchi, 2020. "Modified LASSO estimators for time series regression models with dependent disturbances," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 845-869, December.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:4:d:10.1007_s10260-020-00506-w
    DOI: 10.1007/s10260-020-00506-w
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    References listed on IDEAS

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    1. Medeiros, Marcelo C. & Mendes, Eduardo F., 2016. "ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 191(1), pages 255-271.
    2. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    3. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    4. Marc Hallin & Masanobu Taniguchi & Abdeslam Serroukh & Kokyo Choy, 1999. "Local asymptotic normality for regression models with long-memory disturbance, with statistical applications," ULB Institutional Repository 2013/2091, ULB -- Universite Libre de Bruxelles.
    5. 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.
    6. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    Cited by:

    1. 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.

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