Q1. (Practical Question - Simulations) You may use codes available on the webpage. (a) Generate ARMA(p, q) sequence Xt. You have to choose p, q as well as the required parameters. Make sure that the chosen parameters imply existence of a stationary solution. (b) Identify the model using ACF and PACF. Include graphs of ACF and PACF (2 graphs). (c) Add a linear or a polynomial trend mt. The new sequence is Yt = mt + Xt. (d) Estimate mt using all three methods: parametric method; exponential smoothing; moving average smoothing with your chosen Q. (e) For each of the three methods, plot Yt and t on the same graphs (3 graphs). (f) For each of the three methods, compute X+ = Yt t. Plot residuals (3 graphs). (g) Analyse t using ACF and PACF. Graph ACF and PACF for all three methods (6 graphs). Identify ARMA model. Compare with your identification in (b). Q1. (Practical Question - Simulations) You may use codes available on the webpage. (a) Generate ARMA(p, q) sequence Xt. You have to choose p, q as well as the required parameters. Make sure that the chosen parameters imply existence of a stationary solution. (b) Identify the model using ACF and PACF. Include graphs of ACF and PACF (2 graphs). (c) Add a linear or a polynomial trend mt. The new sequence is Yt = mt + Xt. (d) Estimate mt using all three methods: parametric method; exponential smoothing; moving average smoothing with your chosen Q. (e) For each of the three methods, plot Yt and t on the same graphs (3 graphs). (f) For each of the three methods, compute X+ = Yt t. Plot residuals (3 graphs). (g) Analyse t using ACF and PACF. Graph ACF and PACF for all three methods (6 graphs). Identify ARMA model. Compare with your identification in (b)