In the final exam, there are five exam questions with 20 points each. For each exam question, there are four sub-questions with 5 points each. That’s the basic structure of the final exam. It may be more difficult for Q4 and Q5 comparing to Q1-Q3. Here we give you one example of final exam Q5 which is supposed to be the difficult question.

Please note below example question WON’T be included in the final exam.

Question 5 VECM (maximum total score is 20 points)

a)   Illustrate the Johansen cointegration test based on the VECM below:

b)  Suppose 江 is  3 × 3 matrix and rank(江)=  r. So 江 = aF ′ where  a and  F  are  3 × r vectors. Please illustrate the matrices of a and  F when  r = 2 and write down two co-integration equations in three equations.

c)  A VECM model is proposed to explain the relationship between the natural logs of the daily closing share prices of Pepsi Co and Coca-Cola for the past ten years is estimated using Stata.

Write the cointegrating relationship generated.

d)  Consider the plot of the cointegrating relationship shown below and comment on the fit of the VECM model.

Predicted cointegrated equation -.2             -.1 0               .1               .2
01jan2004          01jan2006          01jan2008          01jan2010          01jan2012          01jan2014 Date