. From FRED, obtain US quarterly imports, seasonally adjusted, in billions of real chained 2012 dollars. The data are available beginning in the first quarter of 1947. The FRED label is IMPGSC1. Create a time variable.
a. For 1947-2000, plot the level of imports and its natural log against time.
b. From your impression of the plot, do you think that the series is best represented by a linear or exponential trend?
c. Estimate an exponential trend model for 1947-2000.
d. Generate point and 90% interval forecasts for the log of imports for 2001-2019.
e. Convert your forecast to levels.
f. Plot your forecasts against the actual data in levels. How did your forecast perform?
g. BONUS: Estimate a linear trend (not an exponential trend) for real imports that accounts for a change in trend in the third quarter of 1983. Generate the points and 90% interval forecasts. Plot against the actual data. Does this forecast perform better than the one that came from the model without the changing trend.