Deck 9: Modelling Volatility and Correlation

Question 1

Which of the following are problems associated with the Engle-Granger approach to modelling using cointegrated data?
(I) The coefficients in the cointegrating relationship are hard to calculate
(ii) This method requires the researcher to assume that one variable is the dependent variable and the others are independent variables
(iii) The Engle-Granger technique can only detect one cointegrating relationship
(iv) Engle-Granger does not allow the testing of hypotheses involving the actual cointegrating relationship.

A) (i), (ii), (iii), and (iv)
B) (ii), (iii) and (iv) only
C) (ii), (iii) only
D) (ii) and (iv) only

Answer 1

(ii), (iii) and (iv) only

Question 2

Which criticism of Dickey-Fuller (DF) -type tests is addressed by stationarity tests, such as the KPSS test?

A) DF tests have low power to reject the null hypothesis of a unit root, particularly in small samples.
B) DF tests are always over-sized.
C) DF tests do not allow the researcher to test hypotheses about the cointegrating vector.
D) DF tests can only find at most one cointegrating relationship.

Answer 2

DF tests have low power to reject the null hypothesis of a unit root, particularly in small samples.

Question 3

To induce stationarity in a deterministic trend-stationary process

A) Regress the non-stationary series on the time trend and use the residuals
B) Difference the series once
C) Difference the series twice
D) No action is necessary because the process is already stationary

Answer 3

Regress the non-stationary series on the time trend and use the residuals

Question 4

Consider the following vector error correction (VECM) model: $\Delta$ y_t = y_t-5 + ₁ $\Delta$ y_t-1 + 11efcd90_39fd_be4b_b057_81d80004b874_TB7071_00₂ $\Delta$ y_t-2 + 11efcd90_39fd_be4b_b057_81d80004b874_TB7071_00₃ $\Delta$ y_t-3 + 11efcd90_39fd_be4b_b057_81d80004b874_TB7071_00₄ $\Delta$ y_t-4 + u_t
Where y_t is a k* 1 vector of variables, and u_t is a k* 1 vector of disturbances.
Which of the following statements is true of the VECM?

A) Johansen's test for cointegration centres on the rank of the matrix 11efcd90_39fd_be4b_b057_81d80004b874_TB7071_00₁
B) If the variables y_t are cointegrated, 11efcd90_16b9_935a_b057_bb82007e6039_TB7071_00 will be of full rank
C) If the rank of 11efcd90_16b9_935a_b057_bb82007e6039_TB7071_00 is zero, the variables are cointegrated
D) Provided that all of the series in y are nonstationary, the rank of 11efcd90_16b9_935a_b057_bb82007e6039_TB7071_00 can be at most k-1.

Question 5

What is the impact of shocks to an AR(1) with no drift if ?

A) Shocks will gradually die away
B) Shocks persist in the system and never die away
C) Shocks will start to increase after the next observation but gradually die away
D) Shocks become more and more influential as time goes on

Question 6

Assuming the researcher in question 19 would like to run an augmented Dickey-Fuller test instead. What is the appropriate regression she would have to run and the null hypothesis of the test?

A) and , respectively
B) and , respectively
C) and , respectively
D) and , respectively

Question 7

The plotted series in the following graph is an example of a:

A) Stationary process
B) Deterministic trend process
C) White noise prices
D) Random walk with drift

Question 8

If the number of non-zero eigenvalues of the pi matrix under a Johansen test is 2, this implies that

A) There are 2 linearly independent cointegrating vectors
B) There are at most 2 linearly independent cointegrating vectors
C) There are 3 variables in the system
D) There are at least 2 linearly independent cointegrating vectors

Question 9

If a Johansen "max" test for a null hypothesis of 1 cointegrating vectors is applied to a system containing 4 variables is conducted, which eigenvalues would be used in the test?

A) The largest 1
B) The Second largest
C) The Second smallest
D) The smallest

Question 10

Which of these is a characteristic of a stationary series?

A) Constant mean
B) Constant autocovariances for each given lag
C) Constant variance
D) All of the above

Question 11

Which one of the following best describes most series of asset prices?

A) An independently and identically distributed (iid, i.e. "completely random") process
B) A random walk with drift
C) An explosive process
D) A deterministic trend process

Question 12

Which of the following are probably valid criticisms of the Dickey Fuller methodology?
(I) The tests have a unit root under the null hypothesis and this may not be rejected due to insufficient information in the sample
(ii) the tests are poor at detecting a stationary process with a unit root close to the non-stationary boundary
(iii) the tests are highly complex to calculate in practice
(iv) the tests have low power in small samples

A) (i), (ii), (iii) and (iv)
B) (i), (ii), and (iv) only
C) (i) and (iii) only
D) (ii) only

Question 13

Which of the following are consequences of using non-stationary data in regressions?
(I) Shocks will be persistent
(II) It can lead to spurious regressions
(III) t-ratios will not follow a t-distribution
(IV) F-Statistic will not follow an F-distribution

A) I only
B) I and II only
C) I, II and III only
D) I, II, III and IV

Question 14

A researcher would like to test for a unit root in a series. She runs the regression . What should her null hypothesis be assuming that she adopts the Dickey-Fuller test approach?

A)
B)
C)
D)

Question 15

Consider the testing of hypotheses concerning the cointegrating vector(s) under the Johansen approach. Which of the following statements is correct?

A) If the restriction is (are) rejected, the number of cointegrating vectors will rise
B) If the restriction(s) is (are) rejected, the number of eigenvalues will fall
C) Whether the restriction is supported by the data or not, the eigenvalues are likely to change at least slightly upon imposing the restriction(s)
D) All linear combinations of the cointegrating vectors are themselves cointegrating vectors

Question 16

If there are three variables that are being tested for cointegration, what is the maximum number of linearly independent cointegrating relationships that there could be?

A) 0
B) 1
C) 2
D) 3

Question 17

Consider the following matrix: What are its characteristic roots?

A) 5 and 0
B) 5 and 5
C) 3 and 2
D) 0 and 0

Question 18

What is the impact of shocks to an AR(1) with no drift if ?

A) Shocks will gradually die away
B) Shocks persist in the system and never die away
C) Shocks will start to increase after the next observation but gradually die away
D) Shocks become more and more influential as time goes on

Question 19

Consider the following data generating process for a series y_t: Which one of the following most accurately describes the process for y_t?

A) A random walk with drift
B) A non-stationary process
C) A deterministic trend process
D) An explosive process.

Question 20

You have the following data for Johansen's $\lambda$ _max rank test for cointegration between 4 international equity market indices: How many cointegrating vectors are there?

A) 0
B) 1
C) 2
D) 3

Question 21

Assume that you are trying to model the relationship between house prices and rents. If you find that both series are non-stationary and a linear combination of the two series is stationary, which of the following is true?
(I) Regressing the levels of house prices on the levels of rents could lead to spurious regressions
(II) House prices and rents are cointegrated
(III) An appropriate linear combination of house prices and rents is I(1)
(IV) House prices and rents are not cointegrated

A) I only
B) I and II only
C) I, II and III only
D) I, II, III and IV only

Question 22

Two variables are said to be cointegrated if

A) If the two variables are I(0) and a linear a combination of the two are I(1)
B) If the two variables are I(1) and a linear a combination of the two are I(1)
C) If the two variables are I(0) and a linear a combination of the two are I(0)
D) If the two variables are I(1) and a linear a combination of the two are I(0)