Fit an appropriate seasonal ARIMA model to the log-transformed Johnson & Johnson earnings series (jj) of Example 1.1 in the textbook. Use the estimated model to forecast the next 4 quarters.

Quarterly Earnings per Share LO 1960 1965 1970 1975 1980 Time Fig. I.I. Johnson & Johnson quarterly earnings per share, 84 quarters, 1960-I to 1980-IV. 1.1 The Nature of Time Series Data Some of the problems and questions of interest to the prospective time series analyst can best be exposed by considering real experimental data taken from different subject areas. The following cases illustrate some of the common kinds of experimental time series data as well as some of the statistical questions that might be asked about such data. Example 1.1 Johnson & Johnson Quarterly Earnings Figure 1.1 shows quarterly earnings per share for the U.S. company Johnson & Johnson, furnished by Professor Paul Griffin (personal communication) of the Graduate School of Management, University of California, Davis. There are 84 quarters (21 years) measured from the first quarter of 1960 to the last quarter of 1980. Modeling such series begins by observing the primary patterns in the time history. In this case, note the gradually increasing underlying trend and the rather regular variation superimposed on the trend that seems to repeat over quarters. Methods for analyzing data such as these are explored in Chapter 2 and Chapter 6. To plot the data using the R statistical package, type the following: - library (astsa) # SEE THE FOOTNOTE plot(jj, type="o", ylab="Quarterly Earnings per Share")