ANSWERS TO EXERCISES 9.3 AND 9.5


EXERCISE 9.3

We have n = 27, k' = 2, d = 0.65, d sub L = 1.24, and d sub U = 1.56.
Because d < d sub L, a significant first-order autocorrelation is
indicated. By Property 9.1, estimates and forecasts are unbiased and
consistent, but inefficient. Tests of hypotheses are invalid and the
goodness of fit is generally exaggerated. A procedure that gives more
efficient estimates is the CORC procedure;

(1) regress LH against a constant, LY, and LP, and save u hat sub t.

(2) compute rho hat from equation (9.7) [you should write this out].

(3) obtain LH sub t sup * = LH sub t - rho hat LH sub t-1,
    LY sub t sup * = LY sub t - rho hat LY sub t-1, and 
    LP sub t sup * = LP sub t - rho hat LP sub t-1.

(4) regress LH sub t sup * against a constant, LY sub t sup *,
    and LP sub t sup * and obtain the parameter estimates and a
    new u hat sub t.

(5) go back to step (2) and iterate until two successive rho hat values
    do not differ much.

EXERCISE 9.5

We have, n = 32, k' = 1, d = 0.207, d sub L = 1.37,
and d sub U = 1.50 . Let the error term be u sub t = rho u sub t-1
 + epsilon sub t where epsilon sub t is "well-behaved." The null
hypothesis is rho = 0 and the alternative is rho > 0 . Because
d < d sub L we reject the null hypothesis and conclude that there
is significant first-order autocorrelation. We are not justified in
feeling that the fit is excellent and that the coefficients are highly
significant. This is because serial correlation makes the tests
invalid and the goodness of fit is generally exaggerated.