= Solution
The MA(1) model has much smaller AIC, $2871.79$ versus $3217.1$, so select \b[MA(1)]. A nominal Wald 95% interval for its non-intercept parameter is
$$
0.9147\pm1.96(0.0130)
=\boxed{[0.8892,\,0.9402]}.
$$
The estimate is close to the noninvertible boundary $\theta=1$, where the regular asymptotic normal approximation becomes poor and likelihood curvature can understate the true one-sided uncertainty. Therefore statement \b[(iii)] is the most plausible: the nominal interval is too narrow to attain its stated coverage reliably.
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