Inference for short-memory time series models based on modified empirical likelihood

Empirical likelihood (EL) has been extensively studied to make statistical inferences for independent and dependent observations. However, it experiences the problem of under-coverage which causes the coverage probability of the EL-based confidence intervals to be lower than the nominal level, especially in small sample sizes. In this paper, we propose modified versions of different EL-related methods to tackle this issue, including the adjusted EL, the EL with theoretical Bartlett correction and the EL with estimated Bartlett correction for short-memory time series models. Asymptotic distributions of the likelihood-type statistics are established as the standard chi-square distribution. Simulations are conducted to compare coverage probabilities with other existing methods under different distributions. Two real data set applications demonstrate how to construct confidence regions of parameters.