Question

Question 5 Original model: R4 = B1 + B2 X RM4 + ut where Rt is the excess return of a U.S. stock (with respect to the risk free rate), RM is the excess return of the S&P500 (with respect to the risk free rate). In order to study the presence of heteroscedasticity, we use the White test (the one indicated in class and used by Brooks (2008)). Consider the following E-Views output (XXXX indicates information that is not included in this table, even though it is part of the standard E-Views output). White Heteroskedasticity Test: F-statistic 0.712712 Obs*R-squared 1.431533 Probability Probability XXXX xxxx Test Equation: Dependent Variable: xxxx Method: Least Squares Included observations: 369 Variable Coefficient Std. Error t-Statistic Prob. XXXX xxxx xxxx xxxx xxxx R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.003879 Mean dependent var 0.000448 -0.001564 S.D. dependent var 0.000839 0.000839 Akaike info criterion -11.31970 0.000258 Schwarz criterion - 11.28791 2091.485 F-statistic XXXX 1.775284 Prob(F-statistic) ХХХХ We focus on the F-test. a) Which is the unrestricted model of this F-test (it is also called the auxiliary regression)? Hint: do not add the cross terms. [7 marks] b) Explain the dependent variable of the unrestricted model. [7 marks] c) Which is the null hypothesis? Which is the restricted model of the auxiliary regression? b) Explain the dependent variable of the unrestricted model. [7 marks] c) Which is the null hypothesis? Which is the restricted model of the auxiliary regression? [7 marks] Page 9 of 13 d) Can we conclude that in the model R+ = B1 + B2 X RM+ + ut there is heteroscedasticity? Test it with 5% of significance level. Depict the graph of the distribution with the critical value and the test statistic. [7 marks] e) Is there an autocorrelation of order 3? The two relevant critical values are 1.7 and 2.3. [7 marks] [Total - 35 marks]