Question 7: [15 marks] Consider the ARX(1) model y: = P1 +f+pyt_1 +6; where the errors follow an AR(2) process er : 1r1 + (1)26\"; + an 1.1 w NHLJZI) fort : 1,. .., T and e_1 : EU : 0. Suppose $1,952 are known. Find (analyt- ically) the maximum likelihood estimators for y, a, p, and 0'2. [Hintz First write y and e in vector/ matrix form. You may wish to use different looking forms for each. Find the distribution of e and y. Then apply some appropriate calculus. You may want to let H : I (plL (1321?, where I is the T X T identity matrix, and L is the lag matrix]