  We propose a sparse coefficient estimation and automated model selection
procedure for autoregressive (AR) processes with heavy-tailed innovations based
on penalized conditional maximum likelihood. Under mild moment conditions on
the innovation processes, the penalized conditional maximum likelihood
estimator (PCMLE) satisfies a strong consistency, $O_P(N^{-1/2})$ consistency,
and the oracle properties, where N is the sample size. We have the freedom in
choosing penalty functions based on the weak conditions on them. Two penalty
functions, least absolute shrinkage and selection operator (LASSO) and smoothly
clipped average deviation (SCAD), are compared. The proposed method provides a
distribution-based penalized inference to AR models, which is especially useful
when the other estimation methods fail or under perform for AR processes with
heavy-tailed innovations (see \cite{Resnick}). A simulation study confirms our
theoretical results. At the end, we apply our method to a historical price data
of the US Industrial Production Index for consumer goods, and obtain very
promising results.
