Economic STATA homework

1. Use aggregate residential investment growth rates from FRED (label A011RL1Q225SBEA). Estimate an AR(4) model for this series.

a. Generate point and interval forecasts for the third and fourth quarters of 2019, and the first and second quarters of 2020 using the direct method. Create a plot of the forecasts and intervals. 3 points.

b. Generate point and interval forecasts for the third and fourth quarters of 2019, and the first and second quarters of 2020 using the iterated method. Create a plot of the forecasts and intervals. Compare the forecasts from the two methods. 3 points.

2. Use household gross fixed investment, residential structures, flow from FRED (label BOGZ1FU155012061Q). Drop all observations before the first quarter of 1952.

a. Convert the series to logarithms and estimate a linear trend. Plot the residuals from the series and discuss. Do you think that the residuals exhibit seasonality and or a cycle component? 2 points.

b. Estimate a model of the log of the series with a linear trend plus seasonal dummy variables. Plot the residuals and discuss. Do you think that the residuals exhibit a cycle component? 2 points.

c. Estimate and AR(4) model with a trend and with or without seasonal dummy variables, depending upon your answers to a and b. Plot the residuals and discuss. 2 points.

d. Using the model in part c, generate point and interval forecasts for the third and fourth quarters of 2019, and the first and second quarters of 2020 using the direct method. Create a plot of the forecasts and intervals. 2 points.

e. What additional adjustments to the forecast model do you think might be appropriate? Why? 2 points.