The U.S. gross national product (GNP) in billions of dollars during the period 1964 to 1984 was as follows:

Year GNP Year GNP 1964 649.8 1975 1,598.4 1965 705.1 1976 1,782.8 1966 772.0 1977 1,990.5 1967 816.4 1978 2,249.7 1968 892.7 1979 2,508.2 1969 963.9 1980 2,732.0 1970 1,015.5 1981 3,052.6 1971 1,102.7 1982 3,166.0 1972 1,212.8 1983 3,401.6 1973 1,359.3 1984 3,774.7 1974 1,472.8 Source: Economic Report of the President, February 1986.

a. Use Holt’s method to predict the GNP. Determine a regression fit of the data for the period 1964 to 1974 to estimate the initial values of the slope and intercept.

(Hint: If you are doing the regression by hand, transform the years by subtracting 1963 from each value to make the calculations less cumbersome.) Using Holt’s method, determine forecasts for 1975 to 1984. Assume that   .2 and   .1.

Compute the MAD and the MSE of the one-step-ahead forecasts for the period 1975 to 1984.

b. Determine the percentage increase in GNP from 1964 to 1984 and graph the resulting series. Use a six-month moving average and simple exponential smoothing with   .2 to obtain one-step-ahead forecasts of this series for the period 1975 to 1984. (Use the arithmetic average of the observations from 1964 to 1974 to initialize the exponential smoothing.)

In both cases (i.e., MA and ES forecasts), convert your forecasts of the percentage increase for the following year to a forecast of the GNP itself and compute the MAD and the MSE of the resulting forecasts. Compare the accuracy of these methods with that of part (a).

c. Discuss the problem of predicting GNP. What methods other than the ones used in parts

(a) and

(b) might give better predictions of this series?