ECONOMICS 7344, Spring 2005
Bent E. Sørensen
March 1, 2005
HOMEWORK 5. Due Monday March 7.
1. Let
xt = α0 + ut + 0.5 ∗ ut−1 + ut−2 ,
where ut is white noise.
Find the autocovariances for xt in terms of σ2u (the variance of ut).
2. Given the AR(1) process
xt = 3 + .4 ∗ xt−1 + .2 ∗ xt−2 + ut
where Eu2t = 2. Is this process stable?
3. Now use the model
yt = ut + 0.5ut−1 ,
where ut is white noise with variance 4.
a) Calculate the variance of yt and the first order autocovariance?
4. Consider the model
yt = ut + 2ut−1 ,
where ut is white noise with variance 0.25.
a) Calculate the variance of yt and the first order autocovariance?
5. Consider again the AR(1) process from question 2. If x0 is a constant use recursive substi-
tution to find the variance of x1 and of x2.
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