Cointegration 1 Exercise 1 Consider two series Yit and Yzt: Yt = IIY+-1 + 6 Or more explicitly as: in which e = [(1, (2]' is IID with E(c) = 0 and E(ce') = 2 8 a) Write the system in levels Answer: b) Show that Yit and Yit are non stationary Answer: The stationary condition for the VAR in levels is that all roots are outside the unit circle: 21 = 1, 22 =- 16 c) Show that II has only one non-zero eigenvalues, and explain this result Answer: Regarding eigenvalues, *1 = 0, 12 = 16 . The explanation please see Lecture notes week 10. d) Show that Yit - 1/8Y2t is the cointegrating vector e) Show that -, ; is the matrix of adjustment coefficients Answer: As we know that, II = aB' = 01 [# #=] If we set B1 = 1, then we obtain the desired result