Question: Suppose that we represent an ARMA (p, q) process as a cascade of a MA (q) followed by an AR (p) model. The input-output equation

Suppose that we represent an ARMA (p, q) process as a cascade of a MA (q) followed by an AR (p) model. The input-output equation for the MA (q) model is:Where ?(n) is a white noise process. The input-output equation for the AR (p) model is:(a) By computing the autocorrelation of v(n), show that:(b) Show that, where ?vx(m) = E[v(n + m)x*(n)]: b w(n - k) v(n) = k=0 x(n) +> arx(n - k)

b w(n - k) v(n) = k=0 x(n) +> arx(n - k) = v(n) k=1 (a) You (m) = ob;bm (b) akYux (m + k) Yer (m) a, = 1

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