Consider the monthly data from the Institute of Supply Management from 1988 to 2012 for exactly 300 observations. The variables used are (a) production index of manufacturing, (b) inventories index, (c) new orders index, and (d) supplier deliveries index. The data are available from FRED of the Federal Reserve Bank of St. Louis and are also in the file m-napm-8812 . txt.

(a) From the data, we have \(\boldsymbol{z}_{151}=(53.7,48.5,52.0,53.9)^{\prime}\). Treat this data point as missing. Build a model for \(z_{t}\) and estimate the missing values.

(b) Suppose that we have \(z_{151}=(53.7,48.5, X, X)^{\prime}\), where \(X\) denotes missing values. Build a model for \(z_{t}\) and estimate the missing values.

(c) Compare the estimates of \(z_{151,3}\) and \(z_{151,4}\) of parts (a) and (b). Comment on these estimates.