ECON1195 Financial Econometrics
Assignment 2
March 2021
This is an individual assignment comprises 25% of the overall assessment.
It consists of Two questions. You need to attempt Both two Questions. This
assignment is based on the relevant course materials (lectures, practice exercises,
R exercises, etc). It covers the lecture materials between week 1 and week 8.
Use 5% level of significance in all hypothesis test questions.
This assignment is due for submission on Canvas by Sunday, 16 May
2021, 11.59PM Melbourne time. Answers can be typed or handwritten
and scanned. You also need submit your R script on Canvas.
Academic Integrity/plagiarism: You can achieve academic integrity by
honestly submitting work that is your own. Presenting work that fails to ac-
knowledge other people’s work within yours can compromise academic integrity.
Submission guidelines: All work for Assessable Tasks is required to be
submitted on the due date and time as outlined in the Assessment Briefs. The
exception to this is where an approved ELS plan, an application for Special
Consideration or an approved Extension of Time is in place, submitted before
the task’s due date with appropriate documentation.
Re-submission: can only be authorised in specific circumstances by formal
RMIT committees. Please visit the RMIT appeals site,
https://www.rmit.edu.au/students/student-essentials/rights-and-responsibilities/appeals,
for information for appealing a grade. Please visit the RMIT website,
https://www.rmit.edu.au/students/student-essentials/assessment-and-results, for
all information regarding adjustments to assessable work.
Late Submission: Work submitted within 7 calendar days of a due (or an
approved amended due) date may be accepted in exceptional circumstances but
will only be assessed as Pass (50%) or Fail. Work submitted beyond 7 calendar
days of a due date will be assessed as 0%.
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Question 1
Let rt denotes the return of a financial asset and σt denotes the standard
deviation of returns at time t,
(a) Write down an AR(1)-ARCH(q) model with q=4.
(b) Write down an AR(1)-GARCH(q,p) model with q=1 and p=2.
(c) Derive the unconditional means of AR(1)-ARCH(4) model and AR(1)-
GARCH(1,2) model in (a) and (b) (Show steps and specify the conditions
if required).
(d) Derive the unconditional variances of AR(1)-ARCH(4) model and AR(1)-
GARCH(1,2) model in (a) and (b) (Show steps and specify the conditions
if required).
(e) Discuss and compare an ARCH(1) model and a GARCH(1,1) model.
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Question 2
In this question, you need choose a stock from ONE of the followings:
1. JPM.csv contains the daily price of JPMorgan Chase & Co;
2. SBUX.csv contains the daily price of Starbucks Corporation;
3. FB.csv contains the daily price of Facebook, Inc;
4. NKE.csv contains the daily price of Nike, Inc.
(a) Explain why you choose this stock (Please do a due diligence of the
company’s background ( your selected company only), Do Not copy
online articles, etc).
(b) Provide appropriate graphs of the continuously compounded returns of
the stock you have chosen to study. Does your return series have the character-
istics that conform to the stylised facts of financial returns data?
(c) Is the stock price stationary?
(d) Obtain the continuously compounded return of the stocks, denoted as
rt, is rt stationary?
(e) Is the return rt consistent with the efficient market hypothesis?
(f) Choose an appropriate model from the ARMA(p,q) family for the returns.
You should justify your choice of model using a relevant criterion for model
selection.
(g) Is there ARCH effect in the returns?
(h) Fit an ARCH(1) model to the return and write down the estimated
model.
(i) Is the ARCH(1) model adequate/well specified?
(j) Fit an ARCH(3) model and write down the estimated model (Show
whether the model is adequate/well specified).
(k) Fit a GARCH(1,1) model, and estimate and write down the estimated
model (Show whether the model is adequate/well specified).
(l) What is “leverage effect” (Provide your own interpretation, Do not
copy from online materials)?
(m) Use an appropriate model to estimate the leverage effect in the data.
Write down the estimated model.
(n) Plot the News impact curve (NIC) from the ARCH(3) model estimated
in (j), the GARCH(1,1) model estimated in (k) and from the model estimated
in (m). Discuss and compare the NIC from these two models.
(o) What is the value for γ1, is the sign consistent with your expectation?
Why?
(p) Conduct the hypothesis test to determine whether the leverage effect is
significant.
(q) What is risk-premium (Provide your own interpretation, Do not
copy from online materials)?
(r) Is the risk-premium present in the data? Use an appropriate model
and test to explain.
(s) Based on the (G)ARCH model used in (j), (k), (m) and (r), which one
do you think is most suitable for your data? Explain.
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