Lasso Guarantees for Time Series Estimation Under Subgaussian Tails and β-Mixing

02/12/2016

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by   Kam Chung Wong, et al.

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Many theoretical results on estimation of high dimensional time series require specifying an underlying data generating model (DGM). Instead, this paper relies only on (strict) stationarity and β -mixing condition to establish consistency of the Lasso when data comes from a β-mixing process with marginals having subgaussian tails. We establish non-asymptotic inequalities for estimation and prediction errors of the Lasso estimate of the best linear predictor in dependent data. Applications of these results potentially extend to non-Gaussian, non-Markovian and non-linear times series models as the examples we provide demonstrate. In order to prove our results, we derive a novel Hanson-Wright type concentration inequality for β-mixing subgaussian random vectors that may be of independent interest.