Consider the following stationary AR(2) process Y = a 413 -1 9231-2 Up, where u, is a white noise process with constant and finite variance o?. Assume that a researcher constructs a variable (a) Show that x can be written as an ARMA(.) process, specifying the lag orders p and 9. 4 marks] (b) Under what conditions is the ARMA process in (a) covariance stationary? [3 marks] (c) Find the mean and variance of the process xt, stating any assumptions used, and showing all your workings. (Hint: Use the obtained mean to calculate the variance). [7 marks] (d) Assume a researcher estimates an AR(2) process to model a stationary variable. However, there is serial correlation left in the error terms of the AR(2) process. How would the researcher test for this, including all the steps and how would he/she account for it? 7 marks]