  This paper considers an augmented double autoregressive (DAR) model, which
allows null volatility coefficients to circumvent the over-parameterization
problem in the DAR model. Since the volatility coefficients might be on the
boundary, the statistical inference methods based on the Gaussian quasi-maximum
likelihood estimation (GQMLE) become non-standard, and their asymptotics
require the data to have a finite sixth moment, which narrows applicable scope
in studying heavy-tailed data. To overcome this deficiency, this paper develops
a systematic statistical inference procedure based on the self-weighted GQMLE
for the augmented DAR model. Except for the Lagrange multiplier test statistic,
the Wald, quasi-likelihood ratio and portmanteau test statistics are all shown
to have non-standard asymptotics. The entire procedure is valid as long as the
data is stationary, and its usefulness is illustrated by simulation studies and
one real example.
