If fxtg and fytg are two uncorrelated stationary processes with autocovariance functions X(_) and Y (_) and spectral densities fX(_) and fY (_), respectively. Show that the process fztg = fxt + ytg is...

If fxtg and fytg are two uncorrelated stationary processes with autocovariance

functions X(_) and Y (_) and spectral densities fX(_) and fY (_),

respectively. Show that the process fztg = fxt + ytg is stationary with autocovariance

function Z = X(_) + Y (_) and spectral density fZ = fX + fY .

Consider the AR(2) process given by: xt = 1:5xt􀀀1􀀀0:75xt􀀀2+4:1+_t.

(a) Is this a stationary process?

(b) Find _x and _x.

(c) Write down and solve the Yule-Walker equations. Calculate _x(3),

_x(4), x(8).