It is an important task in the literature to check whether a fitted
autoregressive moving average (ARMA) model is adequate, while the currently
used tests may suffer from the size distortion problem when the underlying
autoregressive models have low persistence. To fill this gap, this paper
proposes two empirical likelihood-based portmanteau tests. The first one is
naive but can serve as a benchmark, and the second is for the case with
infinite variance innovations. The asymptotic distributions under the null
hypothesis are derived under mild moment conditions, and their usefulness is
demonstrated by simulation experiments and two real data examples.Comment: 23 pages, 2 figure