Consider the quarterly U.S. Federal government debt held by

(a) foreign and international investors and

(b) by the Federal Reserve Banks, in billions of dollars, from 1970.I to 2012.III. Let \(z_{t}\) be the quarterly growth rate series of the debt, that is, the first difference of the log debt.

(a) Specify a VMA model for the growth series of debt.

(b) Fit the specified VMA model and perform model checking.

(c) Write down the fitted model.

(d) Use the model to produce one-step to three-step ahead forecasts of the growth rates of U.S. Federal debt, using the last data point as the forecast origin.