Question

Exercise 5.40 Direct Computation of Acvf for the ARMA(1,2) K, It is not necessary to compute the moving average representation - as was done in Exercise 5.36 in order to get the acvf. We illustrate the technique in the case of the ARMA(1.2). Let Wt-(1 + θ¡B +B2B2)6t be the MA(2) portion with acfr(h), so that Xt is an AR (1) with respect to the (Wt} inputs. Show that EMİXt-h] does not depend on t, and derive an expression for γ(h) in terms of u(h) = Elit Xt-h] and T(h). Simplify, and obtain (1) in terms of the ARMA parameters.

Answer 1

faon .tLe method of ARma the了ǐuen gaatioh is and given that from the Biomia hern Bionam ial expression of 11-φ, s) 8 (4)

, (히 3 1-8 6 2 the weathematical f Une -tio hat .to), φ { B) given by