Again, consider the 14 annual real GDP growth rates, in percentages, of the prior problem.

(a) Perform a model-based clustering analysis with AR order \(p=2\) and 2 clusters.

(b) Standardize the 14 annual real GDP growth rates by computing \(x_{i t}=z_{i t} / \hat{\sigma}_{i}\), where \(\hat{\sigma}_{i}\) is the sample standard deviation of \(z_{i t}\). Repeat the clustering analysis of part (a), but using \(x_{t}\). This type of clustering analysis can be regarded as focusing on the dynamic dependence rather than the variability in classification. Use the command \(\mathrm{xt}=\mathrm{scale}\) ( \(\mathrm{zt}\), center \(=\mathrm{F}\), \(\mathrm{scale}=\mathrm{T}\) ).

(c) Compare the results of the two clustering analysis.