at is white noise with average 0 and variance 1.
a) calculate average and variance MA(2) model
yt = 0,5 + at + 2at-1 -at-2.
Also calculate first three autocorrelation functions, p1, p2 and p3.
b) Calculate average and variance AR(1) model
yt = 1 + 0,5yt-1 +at
Also calculate the first three autocorrelation functions p1, p2 and p3. Hint: To calculate the variance, note that the AR representation zt := yt âˆ’ E[yt] has Î¼ = 0.
c) c) Calculate average AR(2) model,
yt= 1 + 0,75yt-1 + 0,75yt-2 + at.
d) Calculate the average and variance ARMA (1,1) model,
yt = 1 + 0,5yt-1 – at-1 + at.