Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models

In this paper, jackknife empirical likelihood is proposed to be applied in stationary time series models. By applying the jackknife method to Whittle estimator, we obtain new asymptotically independent pseudo samples which will be used to construct linear constraints for empirical likelihood. The jackknife empirical log-likelihood ratio is shown to follow a chi-square limiting distribution, which validates the corresponding confidence regions asymptotically. However, similar to the drawbacks of empirical likelihood, this method suffers from the non-definition problem and the inaccurate coverage probability in constructing confidence regions. So we further develop the adjusted jackknife empirical likelihood borrowing the idea of Chen et al. (2008) to improve the performance of the jackknife empirical likelihood. With a specific adjustment level, the adjusted jackknife empirical likelihood achieves a more high-order coverage precision than the classical jackknife empirical likelihood does and our simulations corroborate this point.