Consider the regression of the US gross domestic product (GDP) on some other economic measures relating to the labor force.

There are various measure of the GDP. We will use the dataset GDP at FRED, which is a quarterly, seasonally-adjusted series begun in 1947 and maintained by the US Bureau of Economic Analysis. For regressors, use

-Unemployment Rate: Aged 15-64: All Persons in the United States LRUN64TTUSQ156S

-Average Weekly Hours of Production and Nonsupervisory Employees: Manufacturing AWHMAN

-Civilian Employment-Population Ratio EMRATIO

-Natural Rate of Unemployment (Long-Term) NROU Information on exactly what these series are can be obtained at the FRED website.

Use all quarterly data from the first quarter of 1987 through the last quarter of 2018. The data obtained from FRED are quarterly except for the monthly data in AWHMAN and EMRATIO, which you must convert to quarterly data.

(a) Fit a linear regression model for GDP on all four regressors listed above.

(b) Analyze the time series of the residuals from the regression fit in Exercise 5.28a.

(c) Based on your analysis of the residuals in Exercise 5.28b, determine an autocorrelation structure, and fit a linear regression model using generalized least squares.

(d) Fit an ARIMA model for GDP with the four regressors as covariates using maximum likelihood, assuming a Gaussian white noise in the ARMA process.