This paper proposes a profile empirical likelihood for the partial parameters in ARMA models with infinite variance. We introduce a smoothed empirical log-likelihood ratio statistic. Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method.
Jinyu Li. Wei Liang. Shuyuan He. "Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance." J. Appl. Math. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/868970