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Academic Honesty
Academic honesty is a core value of the University, and all students are required to act honestly,
ethically and with integrity. The consequences of engaging in plagiarism and academic dishonesty,
along with the process by which they are determined and applied, are set out in the Academic
Honesty in Coursework Policy 2015. Under the same policy, as the unit coordinator, I must report
any suspected plagiarism or academic dishonesty.
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_xfffe_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).
1
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 αMLE, β MLE and σ
2
MLE for the
parameters α, β, and σ
2
Compare αMLE, β MLE with the OLS estimators αOLS, β OLS.
10. In this question, you will use the S&P500 index daily prices1 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 deviation2