 Solution

The MA(1) model has much smaller AIC, $2871.79$ versus $3217.1$, so select MA(1). A nominal Wald 95% interval for its non-intercept parameter isThe 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 (iii) is the most plausible: the nominal interval is too narrow to attain its stated coverage reliably.