Exam 9: Modelling Volatility and Correlation

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

Consider the following matrix: What are its characteristic roots?

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

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

To induce stationarity in a deterministic trend-stationary process

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

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.

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?

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?

Which of these is a characteristic of a stationary series?

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

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 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?

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

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?

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

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

Two variables are said to be cointegrated if

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

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?