A question on unit root in higher order autoregressive models, cointegration, error correction model. See below for details please

A)

(b) Describe the Engle and Granger approach to cointegration in the context of two variables, Yt and Xt. Write down the error correction model for It and explain how this model combines information about the short and long run relationship between the variables. Comment on the sign expected for the adjustment coefficient in the error correction equation for Yt . (8 marks) (c) Suppose you now consider a third variable Zt which is integrated of order one I(1). How would you extend the simple two-variable error correction model described in (b) to include this third variable? (4 marks) (d) Discuss any shortcomings of the Engle and Granger procedure and briefly explain how they could be overcome. (4 marks)Describe ways of testing for (i) one unit root in a first order autoregressive model; (ii) one unit root in higher order autoregressive models. In your answer state clearly the null and alternative hypotheses, and explain how the distribution of the test differs from the conventional t-distribution. (10 marks)