Question ONE {21} hrlrtRKS} You have estimated the following ARMM 1,] } model for some time series data: yr = 13.025 + D.5yt_1 + DZEuFI + u, Suppose that you have data for time to t 1, ie., you know that 3.5-1 = 31}, and {15-1 = 1.5 a} Determine whether the MA part of the process is invertible [show all your workings] (5 Marks] b} If the actual values for the series 1.? for times t, t+ 1J and t + 2 using the estimated ARMA model turned out to be U.d-5, [1865, [i315 for t, t + 1, and t + 2, calculate the out-ofsample mean squared error. {T Marks} c} Describe 3 limitation of ARCpr} models that make researchers prefer GARCH {Ll} models {3 Marks) Question TWD [20 WEEKS] Consider the following vector autoregressive model: I: 1": = ago + thb'rt + \"'5 i=1 Where yr is a p X 1 vector of variables determined by it lags of all 1:: variables in the system, it; is go X 1 vector of error terms, ,8\" is a p X 1 vector of constant term coefcients and ,8; are p X p matrices of coelcients on the :2\"1 lag of Jr. a] If p = 2 and k, = 3. write out all the equations of the VAR in full. carefully dening any new notation you use that is not given in the question. [6 Marks} to Evaluate four main reasons why the 'r'ARs have become popular for application in nance relative to structural equations derived from an underlying theory: [4 Marks}