Expected Value and Auto Covariance for Moving Average Process with Lag h=s-t

[GottaLoveMath]

Homework Statement

Y_t = u_(t-1) + u_(t) + u_(t+1) where u~WN(0,sigma^2)

Find expected value, and auto covariance as a function of lag h = s-t for some s and t

Homework Equations

The Attempt at a Solution

so E(y) = 0

cov(Y_t, Y_h) = cov(u_(t-1) + u_(t) + u_(s-t+1), u_(s-t-1) + u_(t) + u_(s-t+1)

Is this set up correctly, it only really works for s = 2t or something weird like that. [/B]

 

[RUber]

What is the covariance if h=0?
How about h=1?
It looks like it should decrease as h increases.