Let fxt; t 2 Zg a stationary stochastic process with autocorrelation function _x(k). Show that fyt = (1 􀀀 B)xt; t 2 Zg is a stationary stochastic process and calculate _y(k) in terms of _x(k). If xt...

Let fxt; t 2 Zg a stationary stochastic process with autocorrelation

function _x(k). Show that fyt = (1 􀀀 B)xt; t 2 Zg is a stationary stochastic

process and calculate _y(k) in terms of _x(k). If xt is an ARMA (p,q) process,

what can you say about the process rxt?

From the de_nition of the operator r (r = (1 􀀀 B)), _nd expressions

for rzt and r2zt, if zt is de_ned as in the previous exercise what is your guess

about the general expression for rdzt if d > 2?