Use the data in FERTIL3.RAW for this exercise.
(i) Graph gfr against time. Does it contain a clear upward or downward trend over the entire sample period?
(ii) Using the data through 1979, estimate a cubic time trend model for gfr (that is, regress gfr on t, t2, and t3, along with an intercept). Comment on the R-squared of the regression.
(iii) Using the model in part (ii), compute the mean absolute error of the one-step-ahead forecast errors for the years 1980 through 1984.
(iv) Using the data through 1979, regress Δgfrt on a constant only. Is the constant statistically different from zero? Does it make sense to assume that any drift term is zero, if we assume that g/r follows a random walk?
(v) Now, forecast gfr for 1980 through 1984, using a random walk model: the forecast gfrn+1 is simply gfrn. Find the MAE. How does it compare with the MAE from part (iii)? Which method of forecasting do you prefer?
(vi) Now, estimate an AR(2) model for gfr, again using the data only through 1979. Is the second lag significant?
(vii) Obtain the MAE for 1980 through 1984, using the AR(2) model. Does this more general model work better out-of-sample than the random walk model?