In the discussion of Assumption A3 in Section 9.1, computing the mean and variance of the difference in log likelihoods Z = log(f (Y | θ1)) − log(f (Y | θ2)) is suggested for assessing near...

In the discussion of Assumption A3 in Section 9.1, computing the mean and variance of the difference in log likelihoods Z = log(f (Y | θ1)) − log(f (Y | θ2)) is suggested for assessing near nonidentifiability. For example, let θ1 represent the distribution of Y, the MA(1) normal time-series model (see Chapter 4) with parameter θ = −.3, and let θ2 represent the distribution of such a vector from an AR(1) model with parameter φ = .3. Compute the mean and variance of Z (with respect to θ1 as true) and compute a standardized distance t = mean/ √ variance. Although the two models are truly identified, the value of t here is −0.196/ √ 25 for n = 50 (Monahan 1983). Compute similar values for n = 100 using the Levinson–Durbin algorithm.