Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lasso Guarantees for Time Series Estimation Under Subgaussian Tails and
  $ \beta $-Mixing   Many theoretical results on estimation of high dimensional time series
require specifying an underlying data generating model (DGM). Instead, along
the footsteps of~\cite{wong2017lasso}, this paper relies only on (strict)
stationarity and $ \beta $-mixing condition to establish consistency of lasso
when data comes from a $\beta$-mixing process with marginals having subgaussian
tails. Because of the general assumptions, the data can come from DGMs
different than standard time series models such as VAR or ARCH. When the true
DGM is not VAR, the lasso estimates correspond to those of the best linear
predictors using the past observations. We establish non-asymptotic
inequalities for estimation and prediction errors of the lasso estimates.
Together with~\cite{wong2017lasso}, we provide lasso guarantees that cover full
spectrum of the parameters in specifications of $ \beta $-mixing subgaussian
time series. 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 $\beta$-mixing subgaussian random vectors
that may be of independent interest.

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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas