Imports
These data measure imports of goods and services into the United States, quarterly from 1981 through 2011 1n = 124 quarters2. The data are given in billions of dollars, expressed at an annual rate. The data table includes a column named Quarter, with con- secutive values 1, 2, c124, for modeling time trends.
(a) Prior to the recession in 2008, the trend in the value of net imports has a clear bend. Some- times, one can use a log transformation to "take the bend" out of a time series. Does a timeplot of log10 of imports produce a linear trend?
(b) What problems occur if you model the log of imports prior to the fourth quarter of 2008 using a linear trend model? (Regress log10 imports on Quar- ter.) What conditions of the SRM are not satisfied?
(c) As an alternative to trend models, consider using a simpler method: Convert the sequence of im- ports into percentage changes. Does the timeplot of the percentage change prior to the fourth quarter of 2008 appear simple?
(d) Forecast the level of imports for the fourth quarter of 2008, using a model of your choosing. Include a prediction interval for your forecast.
(e) Does your interval include the value for the fourth quarter of 2008?