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Modified LASSO estimators for time series regression models with dependent disturbances

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 \(\lambda\) 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.

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Acknowledgements

The first author would like to thank Mr. Fujimori for helping understand the high dimensional problem-solving idea. The second author thanks supports by Research Institute for Science and Engineering, Waseda University and JSPS Fundings: Kiban(A)(23244011, 15H02061) and Kiban(S)(18H05290).

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Correspondence to Yujie Xue.

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Xue, Y., Taniguchi, M. Modified LASSO estimators for time series regression models with dependent disturbances. Stat Methods Appl (2020) doi:10.1007/s10260-020-00506-w

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Keywords

  • Modified LASSO
  • Long-memory disturbances
  • High dimensional regression