Help in Example 12.10

cov(Xn, Xn+1) = cov(Zn + bZn-1, Zn+1 + bZn) = beta * sigma^2

I am wondering how is this equal to beta * sigma^2

I am unable to solve many other problems just due to confusion in this calculation. Any help will be highly appreciated. Thank!

 

Use Cov(A+B,C) = Cov(A,C) + Cov (B,C)
Cov (kA,B) = k Cov(A,B)
and presumably the Z's are independant so
Cov(Zn,Zn+i) = Var(Zn) if i=0
0 otherwise.

 

Thanks