Empirical Likelihodd Methods for an AR(1) process with ARCH(1) errors

For an AR(1) process with ARCH(1) errors, we propose empirical
likelihood tests for testing whether the sequence is strictly
stationary but has infinite variance, or the sequence is an ARCH(1)
sequence or the sequence is an iid sequence. Moreover, an empirical
likelihood based confidence interval for the parameter in the AR
part is proposed. All of these results do not require more than a
finite second moment of the innovations. This includes the case of
t-innovations for any degree of freedom larger than 2, which serves
as a prominent model for real data.