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LASSO-BASED VARIABLE SELECTION OF ARMA MODELS

Ngai Hang Chan*, Shiqing Ling, Chun Yip Yau

*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

This study considers a least absolute shrinkage and selection operator (Lasso)-based approach to variable selection of ARMA models. We first show that the Lasso estimator follows the Knight-Fu's limit distribution under a general tuning parameter assumption. With a special restriction on the tuning parameters, we show that the Lasso estimator achieves the "oracle" properties: zero parameters are estimated to be zero exactly, and other estimators are as efficient as those under the true model. The results are extended further for nonstationary ARMA models, and an algorithm is presented. In particular, we propose a data-driven information criterion to select the tuning parameter that is shown to be consistent with probability approaching one. A simulation study is carried out to assess the performance of the proposed procedure, and an example is provided to demonstrate its applicability.
Original languageEnglish
Pages (from-to)1925-1948
JournalStatistica Sinica
Volume30
Issue number4
DOIs
Publication statusPublished - Oct 2020
Externally publishedYes

Research Keywords

  • ARMA model
  • information criterion
  • Lasso estimation
  • tuning parameter
  • variable selection

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