The Doubly Adaptive LASSO for Vector Autoregressive Models

  • Zi Zhen Liu
  • Reg KulpergerEmail author
  • Hao Yu
Part of the Fields Institute Communications book series (FIC, volume 78)


The LASSO (Tibshirani, J R Stat Soc Ser B 58(1):267–288, 1996, [30]) and the adaptive LASSO (Zou, J Am Stat Assoc 101:1418–1429, 2006, [37]) are popular in regression analysis for their advantage of simultaneous variable selection and parameter estimation, and also have been applied to autoregressive time series models. We propose the doubly adaptive LASSO (daLASSO), or PLAC-weighted adaptive LASSO, for modelling stationary vector autoregressive processes. The procedure is doubly adaptive in the sense that its adaptive weights are formulated as functions of the norms of the partial lag autocorrelation matrix function (Heyse, 1985, [17]) and Yule–Walker or ordinary least squares estimates of a vector time series. The existing papers ignore the partial lag autocorrelation information inherent in a VAR process. The procedure shows promising results for VAR models. The procedure excels in terms of VAR lag order identification.


Adaptive LASSO Asymptotic normality Estimation consistency LASSO Oracle property Doubly adaptive LASSO PLAC-weighted adaptive LASSO Selection consistency VAR VAR time series Vector auroregressive processes Teacher–Student dual 

Mathematics Subject Classifications (2010)

62E20 62F10 62F12 62H12 62J07 62M10 



We sincerely thank two anonymous referees for their valuable comments and suggestions that we have adopted to improve this manuscript greatly.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsTrent UniversityPeterboroughCanada
  2. 2.Department of Statistical and Actuarial SciencesUniversity of Western OntarioLondonCanada

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