  Empirical likelihood approach is one of non-parametric statistical methods,
which is applied to the hypothesis testing or construction of confidence
regions for pivotal unknown quantities. This method has been applied to the
case of independent identically distributed random variables and second order
stationary processes. In recent years, we observe heavy-tailed data in many
fields. To model such data suitably, we consider symmetric scalar and
multivariate $\alpha$-stable linear processes generated by infinite variance
innovation sequence. We use a Whittle likelihood type estimating function in
the empirical likelihood ratio function and derive the asymptotic distribution
of the empirical likelihood ratio statistic for $\alpha$-stable linear
processes. With the empirical likelihood statistic approach, the theory of
estimation and testing for second order stationary processes is nicely extended
to heavy-tailed data analyses, not straightforward, and applicable to a lot of
financial statistical analyses.
