[SOLVED] BUSI4528 QUANTITATIVE RESEARCH METHODS FOR FINANCE AND INVESTMENT AUTUMN SEMESTER 2019-2020

BUSI4528-E1

A LEVEL 4 MODULE, AUTUMN SEMESTER 2019-2020

QUANTITATIVE RESEARCH METHODS FOR FINANCE AND INVESTMENT

1.  a) In a regression of the U.S. non-farm mortgage debt outstanding on two variables from

1980 to 1995, the following regression results were obtained using Stata:

Debt:      non-farm mortgage debt outstanding in billion $ in the U.S.

Income:  personal income in billion $ in the U.S.

Cost:      new home mortgage cost in %

(i)   Write down the regression model.   [10 marks]

(ii)  Interpret the meaning and significance of each coefficient including the intercept. [20 marks]

(iii) What is the goodness-of-fit of a regression model and what is the F-test for?

Comment on the goodness-of-fit and the F-test results of the above model.   [25 marks]

(iv) Explain the term collinearity. Discuss its consequences in model estimation and explain how to detect it.   [20 marks]

b) Explain  how  graphical  analysis  of  time  series  may  help  to  identify  nonstationary variables.   [25 marks]

Total [100 marks]

2.  a) A sample of 100 workers found the average overtime hours worked in the previous week was 7.8, with standard deviation 4.1 hours. Test the hypothesis that the average overtime hours for all workers is 6.5 hours or less. Use 5% as significance level.

(i) Describe step-by-step the procedure of testing the above hypothesis and state the conclusion.  [30 marks]

(ii) What is p-value? Use the p-value method to test the above hypothesis. [20 marks]

b) Using standard mathematical notation, explain whether the following nonstationary time series models are characterized by deterministic or stochastic trends :

(i)    linear trend model [10 marks]

(ii)   random walk   [10 marks]

(iii)  random walk with drift   [10 marks]

c)  What is meant by ‘spurious regression’? Explain why empirical analysis should be cautious of it.   [20 marks]

Total [100 marks]

3. a) Answer the following questions about panel data modelling.

(i)   Compare and contrast the pooled OLS and fixed effects model in panel data estimation.         [20  marks]

(ii)   Explain the difference between the fixed effects model and the random effects model and how to decide which model is appropriate?                    [30  marks]

b) Consider the following time series model with serially correlated error term:

yt  = α + βxt  + εt ,  with εt   = P1 εt−1  + vt

where var(vt ) = σv(2) ,  and Cov (vt, vs ) = 0  for  t  ≠ S

Show how one could construct a feasible GLS estimator for the parameters α  and β . Discuss the merits of doing so.  [50 marks]

Total [100 marks]

4. a) Answer the following questions about heteroscedasticity.

(i)  Describe what heteroscedasticity is and the consequences of the presence of heteroscedasticity in linear regression.   [20 marks]

(ii) Explain how might the presence of heteroscedasticity be detected and what are the possible solutions to address this issue.  [30 marks]

b) Outline the setup of Probit and Logit models for binary choice data.  [50 marks]

Total [100 marks]

5. a) What does BLUE estimator mean and what are the assumptions to obtain BLUE estimators in a simple linear regression model: y  =  β1  + β2x   +  e  ?   [25 marks]

b) Outline the Dickey-Fuller (DF) test for the null hypothesis of the presence of a unit root in time series.   [25 marks]

c)  Explain how you could test the null hypothesis of no cointegration between two time series variables.   [50 marks]

Total [100 marks]