Show that an AR(p) SDF plus a white noise SDF yields an ARMA(p, p) SDF. As a concrete example find the coefficients for the ARMA(2,2) process obtained by adding white noise with unit variance to the...

Show that an AR(p) SDF plus a white noise SDF yields an ARMA(p, p) SDF. As a concrete example find the coefficients for the ARMA(2,2) process obtained by adding white noise with unit variance to the AR(2) process defined by Equation (34). Plot the SDFs for the AR(2) and ARMA(2,2) processes for comparison.