FN3142
QUANTITATIVE FINANCE
PRELIMINARY EXAM 2018
Question 1
a) When do we say that one forecast \encompasses" another? 30 marks
b) Describe a test for forecast encompassing. 40 marks
c) What null hypotheses would you test to analyse forecast encompassing when there are 3 competing forecasts rather than 2? 30 marks
Question 2
a) Describe using an example what is collective data snooping. 25 marks
b) Describe using an example what is individual data snooping. 25 marks
c) Discuss the differences between collective data snooping and individual data snooping. 25 marks
d) Give two counterexamples to the claim that prices should follow a random walk in an efficient market. 25 marks
Question 3
For VaR calculations at 5% critical level consider using a historical simulation method and a GARCH method for forecasting volatility. After building the so called hit variables
the following regressions are run, where the numbers in parentheses are standard errors for the parameter estimates:
a) Describe how the above regression output can be used to test the accuracy of the VaR forecasts from these two models. 30 marks
b) Based on the above tests what conclusions can you draw. 20 marks
c) Define the violation ratio related to unconditional coverage tests for VaR forecasts. 20 marks
d) If the population violation ratio is defined as VR0 ≡ E[VR], show that testing VR0 = 1 is exactly equivalent to testing E[Hitt] = α. 30 marks
Question 4
a) Define “white noise”. 20 marks
b) What is iid white noise? 20 marks
c) What additional conditions do you need to add such that a white noise Gaussian? 20 marks
d) If {Yt}t≥0 is an AR(1) process, calculate the unconditional variance of Yt. 20 marks
e) For the AR(1) process from part (d) calculate the R2 measure and give an interpretation of the result. 20 marks