Since vt = ut — ut—1, it is easy to show that E(vt) = E(ut — ut—1) = E(ut) — E(ut—1) = 0, since E(u) = 0, for each t. Now, var(vt) = var(ut — ut—1) = var (ut) + var(ut—1) = 2a2, since the variance of each ut is a2 and the us are independently distributed. Hence, vt is homoscedastic. But cov (vt, vt— 1) = E(vtvt—1) = E[(u — ut—1)(ut—1 — ut—2)] = —a 2
which is obviously nonzero. Therefore, although the u's are not autocorre-lated, the v's are.
12A.2 PROOF OF EQUATIONS (12.2.3), (12.2.4), AND (12.2.5)
because the us and e's are uncorrelated.
CHAPTER TWELVE: AUTOCORRELATION 505
Since var (ut) = var (ut—1) = a2 and var(et) = of, we get
Was this article helpful?
Learning About The Rules Of The Rich And Wealthy Can Have Amazing Benefits For Your Life And Success. Discover the hidden rules and beat the rich at their own game. The general population has a love / hate kinship with riches. They resent those who have it, but spend their total lives attempting to get it for themselves. The reason an immense majority of individuals never accumulate a substantial savings is because they don't comprehend the nature of money or how it works.