Answers and explanations as well.

Question 1.1 Consider the following AR(1) Gaussian process for U.S. stock returns: Re+1 = pot pie + et+1 (+1 IID N(0, OF). ou know that po = 1, that E[R +1] = 4, and that Vor [Riti] = 1. Indicate which of the following is/are correct. (A) p, = 0.75 and of = 7/16. (B) p1 = 0.5 and oz = 2/3. (C) p1 = 0.75 and of = 1. (D) p1 = 0.75 and of = 16/7. (F.) None of the aboveWhich of the following statements is/are correct: (A) This VAR(1) model is written in structural form. (B) While 12, has a contemporaneous effect on y1,t, the opposite does not hold. (C) The reduced-form model fails to be identified and restrictions will have to be imposed. (D) The model is just identified. (E) While the structural residuals [e1, (2t] are uncorrelated by construction, the reduced-form residuals [un,t u2, ]' are not. (F) Only if the roots associated to the characteristic equation 0.9 0.2 0.9 0.2 = 0 -0.3 0.7 -0.3 0.7 lie within the unit circle, i.e., all solutions (eigenvalues) A1, A2, .... An are less than 1 in absolute value, the VAR(1) system will be stable. (G) Only if the roots associated to the characteristic equation 0.9 0.2 det = 0 -0.3 0.7 lie within the unit circle, i.e., all solutions (eigenvalues) A1, 12, ..., An are less than 1 in absolute value, the VAR(1) system will be stable. (H) None of the above.Question 1.3 Consider the following restricted VAR(1): if = dot Min_It of where i, is a long-term risk-free rate, i, a short-term risk-free rate, @ and e are white noise shocks. Indicate which of the following is/are correct. (A) For all possible series if and i, then if and only if 72 71 - 1 is a stationary variable (/(0)), we shall say that if and if are cointegrated with cointegration vector [1 - 72/(71 - 1)]'.(B) When both # and if are non-stationary, then if and only if e - e is a non-stationary variable (I(1)), we shall say that if and i are cointegrated with cointegration vector [1 - 1)'. (C) If X1 = 1 and 72 7 0, then both short- and long-term risk-free interest rates are I (1) series. (D) When both is and if are non-stationary, then if and only if 72 71 -1 't-1 is a stationary variable (1(0)), we shall say that * and if are cointegrated with cointegration vector [1 72/(71 - 1)]'. (E) When both & and i" are non-stationary, the first difference of the first equation, Aif = 10+ (71 - 1) ik-1+ 72 71 - 1 represents an error correction mechanism if and only if + 72 5 7-171 ~ I(0) (i.e., if the two rates are cointegrated) and 7