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2020 Nonconcave penalized estimation in sparse vector autoregression model
Xuening Zhu
Electron. J. Statist. 14(1): 1413-1448 (2020). DOI: 10.1214/20-EJS1693

Abstract

High dimensional time series receive considerable attention recently, whose temporal and cross-sectional dependency could be captured by the vector autoregression (VAR) model. To tackle with the high dimensionality, penalization methods are widely employed. However, theoretically, the existing studies of the penalization methods mainly focus on $i.i.d$ data, therefore cannot quantify the effect of the dependence level on the convergence rate. In this work, we use the spectral properties of the time series to quantify the dependence and derive a nonasymptotic upper bound for the estimation errors. By focusing on the nonconcave penalization methods, we manage to establish the oracle properties of the penalized VAR model estimation by considering the effects of temporal and cross-sectional dependence. Extensive numerical studies are conducted to compare the finite sample performance using different penalization functions. Lastly, an air pollution data of mainland China is analyzed for illustration purpose.

Citation

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Xuening Zhu. "Nonconcave penalized estimation in sparse vector autoregression model." Electron. J. Statist. 14 (1) 1413 - 1448, 2020. https://doi.org/10.1214/20-EJS1693

Information

Received: 1 January 2019; Published: 2020
First available in Project Euclid: 1 April 2020

zbMATH: 07200233
MathSciNet: MR4080795
Digital Object Identifier: 10.1214/20-EJS1693

Subjects:
Primary: 62J07 , 62M10
Secondary: 62F12 , 62H12

Keywords: dependent data , High dimensional time series , nonconcave penalization , vector autoregression

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Vol.14 • No. 1 • 2020
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