Simulating ARMA Models Gauss file(s) stsm_simulate.g Matlab file(s) stsm_simulate.m Consider the ARMA(2, 2) model yt = + 1yt1 + 2yt2 + vt + 1vt1

Simulating ARMA Models Gauss file(s) stsm_simulate.g Matlab file(s) stsm_simulate.m Consider the ARMA(2, 2) model yt = µ + φ1yt−1 + φ2yt−2 + vt + ψ1vt−1 + ψ2vt−2, where vt ∼ iid N(0, σ2 v ).

(a) Simulate the following models for T = 200, with the following parameter values Model µ φ1 φ2 ψ1 ψ2 σ 2 v ARMA(0, 0) : 0.0 0.0 0.0 0.0 0.0 0.1 ARMA(1, 0) : 0.0 0.7 0.0 0.0 0.0 0.1 ARMA(2, 0) : 0.0 0.7 −0.5 0.0 0.0 0.1 ARMA(0, 1) : 0.0 0.0 0.0 0.9 0.0 0.1 ARMA(0, 2) : 0.0 0.0 0.0 −0.2 0.7 0.1 ARMA(1, 1) : 0.0 0.8 0.0 0.7 0.0 0.1

(b) Estimate the ACF for each model and interpret the results. Compare the estimated ACF with the theoretical ACF in (13.15).

(c) Estimate the PACF for each model and interpret the results.