70.2K

Verified Solution

Link Copied!

Question 2Consider the following ARMA(2,1)-ARCH(2) model,rt=0+1rt1+2rt2+et+1et1,et=tzt,2t=+1e2t1+2e2t2.(a) For given information available at timet, derive the 1-step, 2-step and 3-step ahead forecasts ofvarianceofrt(show all necessary steps and conditions).(b) If we estimate the model, we obtain0= 0.1,1= 0.3,2=0.15,1= 0.6,= 0.15,1= 0.3 and2= 0.18.Compute thevar(rt=4|It=3),var(rt=5|It=3) andvar(rt=6|It=3) based on theinformation provided in the Table 2.Table 2: Monthly returnstrtet11.512-1.30.832.2-Consider the following GARCH(2,1) model,rt=+et,et=tzt,2t=+1e2t1+2e2t2+12t1,(c) Derive the unconditional variance ofrt,var(rt) (show all necessary stepsand conditions).(d) For given information available at timet, derive the 1-step, 2-step and 3-step ahead forecasts ofvarianceofrt(show all necessary steps and conditions).(e) If we estimate the model, we obtain= 0.85,= 0.28,1= 0.3,2= 0.2 and1= 0.65. Compute thevar(rt=4|It=3),var(rt=5|It=3) andvar(rt=6|It=3) based on the information provided in the Table 3.(f) Comment on the estimated GARCH(2,1) model in (e), is there any issuewith the estimated model? If yes, what is the issue?Table 3: Monthly returnstrtett11.5-1.52-1.3-1.832.2-2.5

DEZE Question 2 Consider the following ARMA(2,1)-ARCH(2) model, T = 60+ 1T-1 + 12-2+ 4 +0,6-1, et o = wta1 + a2c2_z. (a) For given information available at time t, derive the 1-step, 2-step and 3- step ahead forecasts of variance of Te (show all necessary steps and conditions). (b) If we estimate the model, we obtain do = 0.1, 1 = 0.3, 62 = 0.15, 0,= 0.6, w = 0.15, a = 0.3 and Q2 = 0.18. Compute the var(TH|13), var(T=s\/=s) and var ( 16|=) based on the information provided in the Table 2. Table 2: Monthly returns t 1 1.5 1 2 -1.3 0.8 3 2.2 Consider the following GARCH(2,1) model, #+et o = w+are , +azek z+Bho, (c) Derive the unconditional variance of Te, var (T) (show all necessary steps and conditions). (d) For given information available at time t, derive the 1-step, 2-step and 3- step ahead forecasts of variance of re (show all necessary steps and conditions). (e) If we estimate the model, we obtain p = 0.85, w = 0.28, a = 0.3, 02 = 0.2 and 1 = 0.65. Compute the var( 41 ), var( 514 a) and var(re-64-3) based on the information provided in the Table 3. (f) Comment on the estimated GARCH(2,1) model in (e), is there any issue with the estimated model? If yes, what is the issue? Table 3: Monthly returns t . . 1 1.5 - 1.5 2 -1.3 1.8 3 2.2 2.5 DEZE Question 2 Consider the following ARMA(2,1)-ARCH(2) model, T = 60+ 1T-1 + 12-2+ 4 +0,6-1, et o = wta1 + a2c2_z. (a) For given information available at time t, derive the 1-step, 2-step and 3- step ahead forecasts of variance of Te (show all necessary steps and conditions). (b) If we estimate the model, we obtain do = 0.1, 1 = 0.3, 62 = 0.15, 0,= 0.6, w = 0.15, a = 0.3 and Q2 = 0.18. Compute the var(TH|13), var(T=s\/=s) and var ( 16|=) based on the information provided in the Table 2. Table 2: Monthly returns t 1 1.5 1 2 -1.3 0.8 3 2.2 Consider the following GARCH(2,1) model, #+et o = w+are , +azek z+Bho, (c) Derive the unconditional variance of Te, var (T) (show all necessary steps and conditions). (d) For given information available at time t, derive the 1-step, 2-step and 3- step ahead forecasts of variance of re (show all necessary steps and conditions). (e) If we estimate the model, we obtain p = 0.85, w = 0.28, a = 0.3, 02 = 0.2 and 1 = 0.65. Compute the var( 41 ), var( 514 a) and var(re-64-3) based on the information provided in the Table 3. (f) Comment on the estimated GARCH(2,1) model in (e), is there any issue with the estimated model? If yes, what is the issue? Table 3: Monthly returns t . . 1 1.5 - 1.5 2 -1.3 1.8 3 2.2 2.5

Answer & Explanation Solved by verified expert

See Answer