Consider again the population relationship of equation (5.1), y x i i i =α +β +ε .

Assume that this relationship has fourth-order autocorrelation, as specified in equation (9.52):

ε γε ν i i i = + −4 , where νi is the shock for the ith period and γ is a parameter that determines the amount of each disturbance that persists into the fourth subsequent

�period. Correct this population relationship for autocorrelation by constructing a procedure analogous to that at the end of section 9.6.

(a) Rewrite the population relationship between yi and xi for the period i − 4.

(b) Multiply the relationship for the period i − 4 by γ, as in equation (9.30).

(c) Subtract the relationship for the period i − 4, multiplied by γ, from the population relationship for the period i, as in equations (9.31) and (9.32).

(d) Analyze the random component of the resulting relationship. What are its properties? Do they conform to the assumptions of chapter 5 regarding the properties of the disturbances? Why or why not?