Empirical Likelihood Estimation of Levy Processes (Revised in March 2005)
We propose a new parameter estimation procedure for the Levy processes and the class of infinitely divisible distribution. We shall show that the empirical likelihood method gives an easy way to estimate the key parameters of the infinitely divisible distributions including the class of stable distributions as a special case. The maximum empirical likelihood estimator by using the empirical characteristic functions gives the consistency, the asymptotic normality, and the asymptotic efficiency for the key parameters when the number of restrictions on the empirical characteristic functions is large. Test procedures can be also developed. Some extensions to the estimating equations problem with the infinitely divisible distributions are discussed.