Imports These data measure imports of goods and services into the United States, quarterly from 1981 through 2011 (n = 124 quarters). The data are given in billions of dollars, expressed at an annual rate. The data table includes a column named Quarter, with consecutive values 1, 2, . . . 124, for modeling time trends.

(a) Prior to the recession in 2008, the trend in the value of net imports has a clear bend. Sometimes, 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 Quarter.) What conditions of the SRM are not satisfied?

(c) As an alternative to trend models, consider using a simpler method: Convert the sequence of imports into percentage changes. Does the timeplot of the percentage change prior to the fourth quarter of 2008 appear simple, lacking a trend?

(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?