ECMT6006 Applied Financial Econometrics Semester 1, 2023 Assignment 2
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ECMT6006 Applied Financial Econometrics
Semester 1, 2023
Assignment 2
Due: 11.59PM Sunday 30 April 2023
Instructions
• This is an individual assignment which accounts for 10% of your final grade. You may discuss with your classmates, but please ensure that the submitted work is independent.
• You can either hand-write or type your answers, but please compile all your answers in one PDF file and submit it via a file upload in Canvas. You can only submit your work once, so please double check before you submit. The page limit of the submission is 40 pages including appendix (penalty will apply if the page limit is exceeded).
• There are 10 questions (with sub-questions) in this assignment, and please attempt all questions. Detailed solution to each question will be provided after the assignment is due.
• I will randomly select 5 questions (same 5 questions for everyone) to grade, and each question is worth 4 points. The total point of this assignment is 20. The grading will be based on the completion and general quality of your submission.
• For the analytical questions, please show your derivations. Answers without interme- diate steps will be considered as incomplete.
• For the empirical question, please feel free to use any statistical software to answer them. Make sure that you present the required results, including figures, and provide your interpretations if asked. If you use MATLAB live script, you can present your answers in a document (exported from the live script) which contains your code, output, and your explanations in texts. If you use separate code, then please attach your code in an appendix at the end of your submitted PDF file.
• Based on the University late policy, a late submission is subject to a penalty of 5% (of the total points) per calendar day; and work submitted more than 10 days after the due date will receive a mark of zero.
• Patton (2019) refers to the reference textbook by Andrew Patton.
Questions
1. Question 1 in Section 2.7.2 of Patton (2019, p. 66).
2. Question 2 in Section 2.7.2 of Patton (2019, p. 67).
3. Question 4 in Section 2.7.2 of Patton (2019, p. 67–68).
4. Question 2 in Section 4.8.2 of Patton (2019, p. 135).
5. Question 1 in Section 5.10.2 of Patton (2019, p. 185).
6. Question 2 in Section 5.10.2 of Patton (2019, p. 185).
7. Question 3 in Section 5.10.2 of Patton (2019, p. 185).
8. Question 1 in Section 8.6.2 of Patton (2019, p.302).
9. Consider a linear regression model
Yt = α + βXt + et, t = 1, . . . ,T.
We assume that the error terms et are distributed as i.i.d. N(0,σ2 ). Can you derive the maximum likelihood estimators (MLEs), denoted as 
MLE , βˆMLE and 
M(2)LE for the parameters α,β, and σ 2 ? Compare 
MLE , βˆMLE with the OLS estimators 
OLS , βˆOLS .
10. In this question, you will use the S&P500 index daily prices over the period 2010–
2015. Please convert the daily prices into continuously compounded returns, and then use the return series to answer the following questions.
(i) Consider a ARMA(p,q) conditional mean model (allowing for the constant term) for the returns with p = 0, 1, . . . , 5 and q = 0, 1, . . . , 5. Use the three information criteria discussed in class (AIC, HQIC, BIC) to select the best model. Report your results.
(ii) Obtain the residuals from the conditional mean model selected by BIC, and esti-
mate a GARCH(1,1) model using the residuals. Report the estimated parameters in this conditional mean and conditional variance model.
(iii) Plot the estimated conditional volatility in annualized standard deviation.
2023-04-26