  Levy processes are widely used in financial mathematics, telecommunication,
economics, queueing theory and natural sciences for modelling. A typical model
is obtained by considering finite dimensional linear stochastic SISO systems
driven by a Levy process. In this paper we consider a discrete-time version of
this model driven by the increments of a Levy process, such a system will be
called Levy system. We focus on the problem of identifying the dynamics and the
noise characteristics of such a Levy system. The special feature of this
problem is that the statistical description of the noise is given by the
characteristic function (c.f.) of the driving noise not by its density
function. As an alternative to the maximum likelihood (ML) method we develop
and analyze a novel identification method by adapting the so-called empirical
characteristic function method (ECF) originally devised for estimating
parameters of c.f.-s from i.i.d. samples. Precise characterization of the
errors of these estimators will be given, and their asymptotic covariance
matrices will be obtained. We also demonstrate that the arguments implying
asymptotic efficiency for the i.i.d. case can be adapted for the present case.
