(Creating Predicted Level Using Log-Linear Trend Model) To see why it is necessary to correct for the influence of the error term, make sure the MCSim add-in is installed and available; then open a blank Excel workbook and create 400 cells with the formula =NORMALRANDOM(0,1) in column A. In column B exponentiate the numbers in column A by entering the formula

=EXP(A1) in cell B1 and then copying this formula down. Suppose that we wish to find the average value of the exponentiated numbers. Compute three separate estimates of the average of the exponentiated normally distributed random variables. In cell D2 type “=AVERAGE(A1:A400).” In cell E2, type

“=EXP(AVERAGE(A1:A400)).” In cell F2, compute the normal correction factor by typing the formula “ =EXP(STDEV(A1:A400)2/2).” In cell G2, multiply Exp(Ave) by the correction factor by typing in the formula “ =D2*F2.” Figure 21.11.4 shows the setup. Of course we should use the result in cell D2 if we want to know the average of the exponentiated numbers, but how far off would we be if we used the number in cell E2 instead? How much can we improve matters by using the normal correction factor and therefore the number in cell G2?

To answer these questions, run two Monte Carlo simulations, one in which you compare the Exp(Ave) with the Ave(Exp) and a second in which you compare Ave(Exp) with the Corr Factor*Exp(Ave). Comment on your results.
On a separate sheet, create the same setup but use RANDOM() instead of NORMALRANDOM(0,1). How well does the normal correction work in this case?

Year Trend1 Trend2 1970 0 20 1971 1 21 1972 2 22 1973 3 23 1974 4 24 Figure 21.11.1. The first five observations in the data.