N1611 - Financial Econometrics
Self-study Questions #2
1. Consider the following regression:
yt = a + βx2t + ut
(a) Briefly define what is meant by the term 'heteroscedasticity' and explain why there might be a heteroscedasticity in the errors of the model specified above.
(b) What effect does heteroskedasticity in the error process have on the properties and the standard errors of the OLS estimators of α and β? How will this affect the inference we make about the significance of the coefficients?
(c) Describe White's general test for heteroscedasticity.
(d) What are the possible 'solutions' for heteroscedasticity?
2. Consider the model:
Rp;t = β1 + β2RM;t + β3HMLt + β4SMLt + ut
with variables defined as:
Rp;t Excess returns on a portfolio of stocks (portfolio returns minus risk-free rate); RM;t Excess market returns (market returns minus risk-free rate);
HMLt The return of the third most expensive stocks sorted by the market price/book value ratio minus the cheapest third;
SMLt The return of small company stocks minus the return of big company stocks.
(a) Briefly explain the term 'autocorrelation'. Why there might be autocorrelation in the errors of models such as the three-factor model defined above?
(b) What effect does autocorrelation in the error process have on the properties and the standard errors of the OLS estimators of the regression parameters? How will this affect the statistics that are used to test the significance of the coefficients and the model goodness of fit?
(c) Discuss the Breusch-Godfrey procedure for testing for autocorrelation.
3. In the classical linear regression model, we often assume that the error term is normally distributed with mean zero and variance σ2. What are the consequences for the prop-erties of OLS estimators and hypothesis testing if the error term is indeed not normally distributed? Briefly describe the typical causes for the error term to be non-normal and what are the possible solutions.
4. Suppose that the true, but unknown, data generating process is represented by:
gt = β1 + β2x2t + β3x3t + β4x4t + ut ,
but a researcher estimates the model:
gt = β1 + β2x2t + β3x3t + ut.
Briefly describe the implications for the OLS estimates and any statistical inference.
5. Briefly explain what is meant by term 'calendar effects' in the context of financial markets. Give an example.
6. Does the existence of calendar effects in the data contradicts the efficient markets hypothesis?
7. What will be the consequences if calendar effects are present in the data but ignored by the model-building process?
8. What undesirable consequences could arise if the regression model did not include an intercept and the average value of the errors was non-zero?