5. Simulate the following AR(2) processes: Yt=1+0.3 Yt-1 +0.7 Yt-2+ɛtYt-1-0.3 Yt-1 -0.7 Yt-2+εt for øpt → N(0, 1). Comment on their differences: Contrast their time series and their autocorrelation functions. Comment on the covariance-stationary properties of both processes. 41%

solve within 30 mins.

2. Give an example of the time inconsistency problem applied to the relationship of a married couple.

Let A and B be two independent events such that P(A) = 0.25 and P(B) = 0.55- What is P(A or B)? Your answer should be given to 4 decimal places.

Suppose Var(X) = 36, Var(Y) = 42, and X and Y are independent. What is Var(.25X + .75Y)?    Suppose Var(X) = 63, Var(Y) = 87, and X and Y are independent. What is Var(.79X + .21Y)?    Suppose that Var(X) = 907.96, Var(X) = 10219.44, and Cov(X,Y) = 2694.59. What is Var(.33X + .67Y)?

A potential customer has described the following scenario to you:We need to keep track of the data that our manufacturing firm needs to run smoothly.We make a number of products, each of which is manufactured by a different de-partment. Products are made up of a number of parts. Parts are bought fromsuppliers.You have been asked to perform a preliminary analysis of the scenario:a) Identify four sets of values from the scenario. b) Identify three relations from the scenario. c) Draw an entity-relationship diagram to visualise the sets and relations you have identi-fied. d) Use the relations you identified in part b) to define the following:i) A relation that records the parts that a department needs. ii) A relation that records the suppliers that a department deals with

1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3

4- The manager of Collins Import Autos believes the number of cars sold in a day(Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working that day (S ). After collecting data for two months (53 days), the manager estimates the following log-linear model: Q = aHbSc ----- a. Explain how to transform this log-linear model into a linear form that can be estimated using multiple regression analysis. b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance level.

18. A multiple regression model, K = a + bX + cY + dZ, is estimated regression software, which produces the following output: D. If X equals 50, Y equals 200, and Z equals 45, what value do you predict K will take?

Which of the following statements is true under the Gauss-Markov assumptions? a. Among a certain class of estimators, OLS estimators are best linear unbiased but are asymptotically inefficient. b. Among a certain class of estimators, OLS estimators are biased but asymptotically efficient. c. Among a certain class of estimators, OLS estimators are best linear unbiased and asymptotically efficient. d. The LM test is independent of the Gauss-Markov assumptions. O a. a O b. b О с. с O d. d