. In Exercise 13.22, you fitted a linear trend model to the year-to-year changes in world reserves of gold held by governments.
(a) Let yt be the amount of world reserves for period t. Reexpress the trend model for changes to give a predictive equation for yt .
(b) Use the predictive equation from part (a) to get the fitted values for the world reserves series for periods 2, 3, . . . , 27.
(c) Superimpose the fitted values from part (b) on the annual world reserve data series plotted in part (a) of Exercise 13.21.
(Note: When plotting the fitted values, remember that they start with period 2, while the original series starts with period 1.)
(d) Make a time series plot of the residuals from the linear trend fit and perform the runs test on the residuals. What is your conclusion in terms of how well the model fits the data series?
(e) How do you interpret the linear trend model of changes as it relates to the original data series on world holdings of gold