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2018 Variable screening for high dimensional time series
Kashif Yousuf
Electron. J. Statist. 12(1): 667-702 (2018). DOI: 10.1214/18-EJS1402


Variable selection is a widely studied problem in high dimensional statistics, primarily since estimating the precise relationship between the covariates and the response is of great importance in many scientific disciplines. However, most of theory and methods developed towards this goal for the linear model invoke the assumption of iid sub-Gaussian covariates and errors. This paper analyzes the theoretical properties of Sure Independence Screening (SIS) (Fan and Lv [20]) for high dimensional linear models with dependent and/or heavy tailed covariates and errors. We also introduce a generalized least squares screening (GLSS) procedure which utilizes the serial correlation present in the data. By utilizing this serial correlation when estimating our marginal effects, GLSS is shown to outperform SIS in many cases. For both procedures we prove sure screening properties, which depend on the moment conditions, and the strength of dependence in the error and covariate processes, amongst other factors. Additionally, combining these screening procedures with the adaptive Lasso is analyzed. Dependence is quantified by functional dependence measures (Wu [49]), and the results rely on the use of Nagaev-type and exponential inequalities for dependent random variables. We also conduct simulations to demonstrate the finite sample performance of these procedures, and include a real data application of forecasting the US inflation rate.


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Kashif Yousuf. "Variable screening for high dimensional time series." Electron. J. Statist. 12 (1) 667 - 702, 2018.


Received: 1 May 2017; Published: 2018
First available in Project Euclid: 27 February 2018

zbMATH: 06864473
MathSciNet: MR3769192
Digital Object Identifier: 10.1214/18-EJS1402

Primary: 62F07
Secondary: 62J07

Keywords: functional dependence measure , High-dimensional statistics , Lasso , Nagaev inequality , Sparsity , sure independence screening , time series , Variable selection


Vol.12 • No. 1 • 2018
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