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Financial Econometrics ASB 4408-Bangor Business School - Prifysgol Bangor University | 2017 Past paper solutions

ALL questions in Section A and THREE questions in Section B

SECTION A Answer ALL questions. Section A carries 40% of the total mark
(4 marks per question).

A1. Which of the following is the correct definition of the p-value of a hypothesis test?

A. The probability of rejecting the null hypothesis when the null is false.
B. The probability of accepting the null hypothesis when the null is true.
C. The minimum significance level at which the null hypothesis can be
accepted.
D. The maximum significance level at which the null hypothesis can be
accepted.
E. The minimum significance level at which the null hypothesis can be
rejected.

Answer: E (Purchase past paper to get the full solution)

A2. Which of the following statements is FALSE?

A. The product of a 3×5 matrix and a 5×3 matrix is a 3×3 matrix.
B. The product of a 3×5 matrix and a 5×2 matrix is a 5×5 matrix.
C. The product of a 3×5 matrix and a 3×5 matrix is not defined.
D. The sum of a 3×5 matrix and a 3×5 matrix is not defined.
E. Both B and D.

Answer: E (Purchase past paper to get the full solution)

A3. Which of the following is NOT a necessary assumption underlying Ordinary Least Squares
(OLS) estimation of the coefficients of a linear regression?

A. The error term is homoscedastic.
B. The error term is normally distributed.
C. The error term is random.
B. The true relationship between the explanatory variable and the dependent
variable is linear.
D. The explanatory variable is exogenous.

Answer: B (Purchase past paper to get the full solution)

A4. When the exogeneity assumption is invalid in the two-variable linear regression model 
which of the following statements is TRUE?

A. There is backward (reverse) causality from yi to xi.
B. There is backward (reverse) causality from yi to ui.
C. The OLS estimators of ?1 and ?2 are efficient.
D. The covariance between xi and ui is zero.
E. ui is heteroscdastic and serially correlated.

Answer: A (Purchase past paper to get the full solution)

A5. The determinant of the square matrix 

A. 13
B. 19
C. 22
D. 32
E. 40

Answer: D (Purchase past paper to get the full solution)

A6. The trace of the square matrix 

A. 13
B. 19
C. 22
D. 32
E. 40

Answer: A (Purchase past paper to get the full solution)

A7. You have fitted a cross-sectional regression using n=30 observations, and you have then estimated an auxiliary regression of the squared residuals on the squared fitted values. The R² value in the auxiliary regression is 0.16. What do you infer from this result?

A. The residuals from the cross-sectional regression are homoscedastic.
B. The residuals from the cross-sectional regression are free of serial correlation.
C. The residuals from the cross-sectional regression are not normally distributed.
D. The residuals from the cross-sectional regression are heteroscedastic.
E. The residuals from the cross-sectional regression are serially correlated.

Answer: E (Purchase past paper to get the full solution)

A8. You have downloaded from Datastream historical share price data for a company. Which among the following tests would be useful to understand whether the series is stationary or non-stationary?

A. Im, Pesaran and Shin (IPS) test.
B. White test.
C. Engle-Granger test.
D. Augmented Dickey-Fuller test.
E. Ljung-Box test.

Answer: D (Purchase past paper to get the full solution)

A9. The asymmetric GARCH model is applicable in which of the following cases:

A. The distribution of the residuals is positively or negatively skewed.
B. A negative shock exerts a bigger influence on the conditional variance than a
positive shock of the same absolute magnitude.
C. The conditional variance is non-stationary.
D. The explanatory variable is non-stationary, but the dependent variable is stationary.
E. The residuals exhibit volatility clustering and excess kurtosis.

Answer: B (Purchase past paper to get the full solution)

A10. The variables yt and xt are both non-stationary, but the residuals from the regression of y_t on
x_t are stationary. Which of the following is correct?

A. The residuals from the regression of y_t on x_t are normally distributed.
B. The residuals from the regression of y_t on x_t are free of serial correlation.
C. x_t and y_t are cointegrated.
D. There is no long-run relationship between x_t and y_t.
E. None of the above.

Answer: C (Purchase past paper to get the full solution)

SECTION B Answer THREE questions. Section B carries 60% of the total mark
(20 marks per question).

B1. (a) Explain what is meant by the following terms:

(i) Heteroscedasticity.
(ii) Serial correlation.
(6 marks)

(b) With reference to the multiple regression model, explain how you could test for the presence of serial correlation. (7 marks)

(c) Explain what is meant by a spurious regression problem.(7 marks)

B2. (a) Explain what is meant by an endogeneity problem. (6 marks)

(b) With reference to instrumental variables regression, explain the following terms:

(i) Instrument relevance.
(ii) Instrument exogeneity.

(6 marks)

(b) In a regression model where one of the explanatory variables is endogenous rather than exogenous, explain how an instrumental variables regression estimated using two stage least squares (2SLS) can be used to obtain consistent estimates of the regression coefficients. (8 marks)

B3. Using 53 yearly observations for the period 1953-2005 inclusive on y_t = natural logarithm of the UK retail price index, a researcher has obtained the following results by estimating three ADF (Augmented Dickey Fuller) autoregressions:

(a) Using these results, determine the order of integration of the series yt. (8 marks)
(b) What are the likely consequences for the performance of the ADF test if an inappropriate number of lagged values of Δy_t–j is included in the ADF autoregressions? (12 marks)

B4. (a) Explain the following terms:

(i) White noise.
(ii) Integrated of order one. (8 marks)

(b) With reference to the following VAR(1) model:

(6 marks)

(c) With reference to the following VAR(2) model:

(6 marks)

B5. (a)

(i) Describe the method developed by Engle and Granger to test for the existence of a cointegrating relationship between two non-stationary time series variables.
(ii) Explain how a cointegrating relationship is incorporated into the specification of an Error Correction Model.
(10 marks)

(b) Following Johansen’s methodology, the following VECM (Vector Error Correction Model) has been proposed to model the relationship between the non-stationary time series variables y_1t and y_2t:

(10 marks)

B6. Consider the following AR(1)-GARCH(1,1) model for the series y_t:

Using daily data from 01/01/2004 to 31/12/2013, a researcher has obtained the following estimated version of this model for y_t = daily logarithmic return on the FTSE100 index:

Standard errors of the estimated coefficients are shown in parentheses.

(a) Comment briefly on your interpretation of the estimated values of the coefficients a₁ and b₁. (5 marks)
(b) Describe a test you could use to determine whether the fitted model adequately describes the daily FTSE100 logarithmic returns series. (7 marks)

B7. (a) You have obtained cross-sectional data on scores in a financial literacy test for a group of individuals who have either participated or not participated previously in a financial literacy training program. The decision to participate is believed to depend on past educational attainment and other personal characteristics of the participants, which may also influence performance in the test, and which are also recorded in the data set.

Explain how a propensity score matching estimator could be used to evaluate the effectiveness of the financial literacy training program. (10 marks)
(b) Explain how difference-in-differences estimation using panel data can assist in evaluating the impact of an exogenous policy or regulatory change. (10 marks)

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Last updated: Oct 03, 2019 09:17 AM