Reference no: EM132525322 , Length: word count:2000

Part A - Answer ALL questions. Each question has only ONE correct answer.

1. If the value of an estimator approaches the true population value as the sample size increases, the estimator is:

Unbiased
Biased
Consistent
Efficient

2. What does the intercept coefficient represent in the following population regression function (PRF)?
Y_i=β_1+β_2 X_i+u_i

the expected value of Y given X = 0
the change in Y per unit change in X
the fixed value of X
the variation of X around its own mean value

3. Which of the following is the value of b1 in the estimation results based on the Ordinary Least Squares (OLS) method?
Y_i=b_1+b_2 X_i+e_i

whereX ¯=10.546,Y ¯=15,b_2=-0.363

18.828
15.991
3.828
5.445

4. In the Classical Linear Regression Model (CLRM) what does the following assumption stand for?
cov(u_i,X_i )=0 for all i=0,...,N

The mean value of the error term is zero
The error term has a constant variance
The errors and the independent variables Xi's are likely to co-move
The errors and the independent variables Xi's are independent

5. In the following regression model: lnY_t=β_1+β_2 lnX_t+u_twhat does β2 represent?

The elasticity of Y with respect to X
The rate of change of Y with respect to X
The growth rate of Y over time
The value of Y given that X = 0

6. A researcher has estimated a multiple regression model with three independent variables and 80 observations. The value of the coefficient of determination (R2) is 0.7. What is the value of the adjusted R2?

0.727
0.288
0.326
0.688

7. Which of the following defines ‘structural break' in regression analysis?

changes in the parameter values of the regression model
invalid estimation results when using the OLS estimation method
invalid Classical Linear Regression Model (CLRM) assumption
None of the above

8. Under the imperfect multicollinearity

the OLS estimator cannot be computed.
the error terms are highly, but not perfectly, correlated.
two or more of the regressors are highly correlated.
All of the above

9. The Durbin-Watson (DW) test is applied to a regressioncontaining three explanatory variables plus a constant with 80 data points. The DW test statistic takes a value of 2.24. What is the appropriate conclusion at the 5 percent significance level?

Residuals appear to be positively autocorrelated
Residuals appear to be negatively autocorrelated
Residuals appear not to be autocorrelated
The test result is inconclusive

10. What would be the consequences for the OLS estimator if heteroscedasticity is present in a regression model, but is ignored?

It will be biased
It will be inconsistent
It will be efficient
It will be unbiased and consistent

11. Which of the following will result from including an irrelevant variable in a model?

The OLS estimates are still unbiased and consistent.
The hypothesis testing procedures remain valid.
The parameter estimates will be generally inefficient.
All of the above

12. Stationarity means that the

error terms are not correlated.
distribution of the time series variable does not change over time.
time series has a unit root.
time series are a random walk.

13. Which of the following are characteristics of a White Noise process?
It has constant mean and variance
It contains trend component
It crosses its mean value frequently
It may be stationary in first difference form

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

14. The AR(p) model

is defined as Y_¬ ¬_t=β_0+β_p Y_(t-p)+u_t
represents Yt as a linear function of p of its lagged values and an error term.
can be represented as follows: Y_¬ ¬_t=β_0+β_1 X_t+β_p Y_(t-p)+u_t
can be written as follows: Y_¬ ¬_t=β_0+β_1 X_(t-p)+β_p Y_(t-p)+u_t

15. Which of the following features in the volatility of financial time-series are captured by a standard GARCH (1,1) model?
Time-varying
Mean-reverting
Clustering
Asymmetric

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

Part B - Answer any TWO questions.

Using monthly log return data over the last ten years, a researcher uses Ordinary Least Squares regression analysis to estimate a regression model of the TESCO stock return on the FTSE100 Index return, the Sainsbury return and the ASDA return. The following estimated equation is reported (the standard errors are given in brackets).

?TESCO?_t=0.008612+0.3399 ?FTSE?_t+0.3386? SAINS?_t+0.2835 ?ASDA?_t+e_t
(0.004978) (0.1283) (0.07709) (0.0572)

where the number of observations is 120 and R2 = 0.2796.
Using the conventional testing procedures and statistical tables provided:

Test the significance of the partial slope coefficients estimated by the model.

Test the overall significance of the model.

Interpret the estimated model and comment on the results.

A second version of the model is also estimated in which SAINS and ASDA have been removed from the regression. This model gives the estimated equation:
?TESCO?_t=0.05873+0.4278 ?FTSE?_t+e_t
(0.00273) (0.1733)
where R2 = 0.2136

Explain how you would test for the restrictions on the parameters of the first version of the model, using the first and the second versions of the model regression results. Stating the null and alternative hypotheses of your test, carry out an appropriate test to identify the preferred model.

Explain what is meant by dummy variables and how you would use a dummy variable to examine the impact of Brexit referendum in June 2016 on TESCO's stock return.

17. What is meant by the coefficient of determination (R^2)? Why theR^2 is not an accurate measure of goodness of fit in multiple regression models? How could you remedy this problem?

Using appropriate notation, explain the Chow test for structural break.

Given the true model is:
Y_i=β_1+ β_2 X_2i+ β_3 X_3i+ u_i
where: Y_i= consumption expenditure, X_2i= disposable income, X_3i= accumulated wealth. Suppose you mistakenly added an irrelevant variable (X_4i) to the model. Discuss the possible consequences of such a misspecification. (30 marks)

18. Discuss the nature and importance in financial econometrics of TWO of the following:
Multicollinearity
Autocorrelation
Stationarity
ARCH models

19. A researcher estimates the following model for stock market returns, but thinks that there may be a problem with it. By calculating the t-ratios, and considering their significance and by examining the value of R2 or otherwise, suggest what the problem might be.
•(Y ^_t=?0.638+0.402X?_2t-0.891X_3t&R^2=0.96,)R ¯^2=0.89
•((0.436)&(0.291)&(0.763) )
How might you go about solving the perceived problem?

State in algebraic notation and explain the assumption about the CLRM's disturbances that is referred to by the term ‘homoscedasticity'.

What would the consequence be for a regression model if the errors were not homoscedastic?

How might you proceed if you found that (c) were actually the case?

20. Define the term "unit root" and explain why it isimportant to test for unit root in time series data before attempting to build an empirical model.

A researcher wants to test for the presence of unit root in time seriesdata and decides to use the Dickey-Fuller (DF) test. He estimates a regression of the form
??y?_t=μ+ψy_(t-1)+u_t

and obtains the estimate ψ ^=-0.52with standard error = 0.16

Given the data, and a critical value of -2.88, perform the DF test.What are the null and alternative hypotheses for this test?What is the main conclusion from this test?

Another researcher suggests that there may be a problem with this methodology since it assumes that the disturbances (ut) are white noise. Suggest a possible source of difficulty and how the researchermight in practice get around it.

Attachment:- Financial Econometrics.rar