Question 1 Let rt denotes the return of a financial asset and ot denotes the standard deviation of returns at time t. If rt follows an ARMA(2,2) model, rt = 00 + oirt-1 + 2rt-2 +et +0jet-1 +02et-2, (a) Derive the unconditional mean of rt, E(rt) (show all necessary steps and conditions) (b) For given information available at time t, derive the 1-step, 2-step and 3-step ahead forecasts of rt (show all necessary steps and conditions). (c) If we estimate the ARMA(2,2) model, we obtain 0o = 0, $1 = 0.5, 02 = 0.2, 01 = -0.8 and 02 = 0.6, compute the E(Tt=3|1=2), E(Tt=4|1=2) and Ert=5|1=2) based on the information provided in the Table 1. Table 1: Monthly returns t 1 3.1 0.3 2 - 1.1 0.5 3 ? 4 ? 5 ? Question 1 Let rt denotes the return of a financial asset and ot denotes the standard deviation of returns at time t. If rt follows an ARMA(2,2) model, rt = 00 + oirt-1 + 2rt-2 +et +0jet-1 +02et-2, (a) Derive the unconditional mean of rt, E(rt) (show all necessary steps and conditions) (b) For given information available at time t, derive the 1-step, 2-step and 3-step ahead forecasts of rt (show all necessary steps and conditions). (c) If we estimate the ARMA(2,2) model, we obtain 0o = 0, $1 = 0.5, 02 = 0.2, 01 = -0.8 and 02 = 0.6, compute the E(Tt=3|1=2), E(Tt=4|1=2) and Ert=5|1=2) based on the information provided in the Table 1. Table 1: Monthly returns t 1 3.1 0.3 2 - 1.1 0.5 3 ? 4 ? 5