Test Bank Questions Chapter 7

Multiple Choice Test Bank Questions No Feedback – Chapter 7 Correct answers denoted by an asterisk. 1. 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 nonstationary 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 2. 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 3. Consider the following vector error correction (VECM) model: yt = yt-5 +  1yt-1 +  2yt-2 +  3yt-3 +  4yt-4 + ut where yt is a k  1 vector of variables, and ut 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  1 (b) If the variables yt are cointegrated,  will be of full rank (c) If the rank of  is zero, the variables are cointegrated (d) * Provided that all of the series in y are nonstationary, the rank of  can be at most k-1. 4. Consider the following matrix:

 3 X   1

6 2 

What are its characteristic roots? (a) * 5 and 0 (b) 5 and 5 (c) 3 and 2 (d) 0 and 0 5. You have the following data for Johansen’s max rank test for cointegration between 4 international equity market indices: r 5% Critical Value max 0 40.03 30.26 1 26.81 23.84 2 13.42 17.72 3 8.66 10.71 How many cointegrating vectors are there? (a) 0 (b) 1 (c) * 2 (d) 3 6. 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. 7. Consider the following data generating process for a series yt: y t    1.5 y t 1  u t

Which one of the following most accurately describes the process for yt? (a) (b) (c) (d)

A random walk with drift A non-stationary process A deterministic trend process * An explosive process.

8. 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

9. 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 10. 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 11. 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 12. 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