Proof of strictly stationary process

[trenekas]

Hi all. I need to prove or disprove if process Y_n=1/2*X_n+1/4*X_{n-1}+1/8*X_{n-2} are stricly stationary. X_n,n\in R i.i.d.
So almost i have the answer. But don't know if it is correct or not. I have a question of situation when \Gamma_Y(t,s) and |t-s|≤2 for example:
Y_{10}=1/2*X_{10}+1/4*X_{9}+1/8*X_{8}
Y_8=1/2*X_8+1/4*X_{7}+1/8*X_{6}
There are x_8 in both but situations and not sure if Y_{10} and Y_{8} are i.d.
Hope you understand my problem.
Maybe its a little stupid question but I'm just started to learn random processes. :)
Thanks for help.

 

[mathman]

The Y's will be correlated as you noticed. The correlation depends only on the parameter difference.
However, the distributions will be identical, since the X's have identical distributions.

Put these together and you get strictly stationary.