Financial statistics Model

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 − E[yt] has μ = 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.

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