1

ECON90033 Semester 2, 2025 Assignment 2
ECON90033 – QUANTITATIVE ANALYSIS OF FINANCE I
Second Semester, 2025
Assignment 2
Due date and time: Friday 10 October, 11:00AM


Please read the following instructions carefully before starting to work on the
assignment.
 There is a total of 50 marks for this assignment. It is worth 25% of the final
grade for QAF1.
 This assignment must be submitted online via the LMS by 11:00AM on
Friday 10 October. Any assignment not submitted by the due date and time
will incur a penalty of the available marks: namely, 10% penalty for 1-60
minutes late, 20% penalty for 61-120 minutes late, 30% penalty for 121-180
minutes late, etc., until zero mark.
 Students may work alone and submit their own assignment answers if they
wish to do so, or they can work on the assignment in pairs. In the latter case,
each assignment pair must submit only one set of assignment answers, and
both students of the pair will receive the same mark for their assignment. It
is not allowed to form assignment groups of more than two students.
 Please note that the assignment submission process has two stages:
1. Registering your assignment group (only if you work in a pair), and
2. Submitting the assignment online via the LMS.
Students who intend to work on the assignment in pairs must register their
groups. To do so, click the “People” link and then the Groups tab in the
Canvas course navigation menu. The group names (set by default) are A2
Group 1, A2 Group 2, A2 Group 3, etc. Every assignment pair MUST register
as one of these created groups for submitting the assignment and not create
a new group. The deadline for registering your group is 5:00PM on Friday 3
October. If a pair fails to register their group before the deadline for group
registration, both students will need to make an individual, i.e., sufficiently
different, submission.
Students making individual submissions do not need to register.
 Answer the assignment questions using Microsoft Word or some other word
processing software (WordPerfect Office, LaTeX, R markdown, Scientific
Work, etc.). Make sure to include a cover page in the document with the
student ID, the name, and the tutorial group of each group member.
 If a task involves some manual calculations, use your calculator (not R,
Excel, or any other software), the relevant statistical table(s), and show the
2

ECON90033 Semester 2, 2025 Assignment 2
major steps, including the formulas in the document. Otherwise, use only R
/ RStudio and paste your scripts, screenshots, and printouts (graphs, output
tables, etc.) into the document.
 Once you complete the assignment, convert the whole file to PDF before
submitting it online via the LMS. Please note that only PDF files can be
uploaded to the LMS.
 Do not forget to preview your assignment after uploading it on the LMS to
ensure that you have indeed uploaded the correct and complete assignment
and that its formatting is in order as in the original document. Submissions
that are late because of formatting issues or because a version is
incomplete, will not be accepted.


Assignment Tasks and Questions
Download the a2e1.xlsx file. There are three exercises in this assignment, each
consisting of several parts. Every exercise and part is compulsory. For every
test you are asked to perform and comment on, state the hypotheses, make a
statistical decision with explanation, and state your conclusion. Be precise and
explain your statements and answers.

Exercise 1 (21 marks = 4 + 6 + 10 + 1)
The data saved in the a2e1.xlsx file are daily closing prices of the Hang Seng Index
(HSI) from 2 January 2004 to 29 February 2024.

Launch RStudio, create a new project and script, and name both a2e1. Import the data
from the a2e1.xlsx file to RStudio and save them as a2e1.RData. Attach this data set
to your R project and create a HSI xts object.

a) Calculate the daily log returns of the Hang Seng Index (r), illustrate it with a nicely
customised (title, label, colour) time-series plot and briefly describe the historical
data pattern.

b) Perform the appropriate DF  and  tests on r. Use the min(10, T/5) rule of thumb
to determine the largest lag allowed in the test regression and select the optimal
lag length by minimising AIC. Do you have any deterministic term in the test
regression? Explain your decision. Evaluate the results at the 1% significance
level.


3

ECON90033 Semester 2, 2025 Assignment 2
c) Perform the PP Z-tau, ERS DF-GLS, SP, KPSS, and ZA tests on r at the 1%
significance level. Use the same number of lags in the ERS and ZA tests as in the
ADF tests in part (b).1

d) Considering all the unit root / stationarity tests in parts (b) and (c), what overall
conclusion can you draw?


Exercise 2 (12 marks = 9 + 3)
Launch RStudio, create a new project and script, and name both a2e2. Import the data
from the a2e1.RData file, save it as a2e2.RData, attach it to your R project, and
calculate the daily log returns of the Hang Seng Index (r).

a) Search for the best fitting ARIMA model for r. Use the auto.arima() function with
the ic = “aicc”, seasonal = FALSE, approximation = FALSE, stepwise = FALSE,
trace = TRUE arguments. In addition, depending on your answer in part (d) of
Exercise 1, set the d argument equal to 0 or 1.

Given the best fitting model,

i. Write out the sample regression equation in the standard form.
ii. Check the residuals for autocorrelation and normality at the 5% level.
iii. Perform t-tests for the significance of the AR and MA coefficients of this
model at the 5% level.

b) Use the best fitting model in part (a) to forecast r for 1 to 5 days ahead following
the last day in the sample period. Print your point and interval forecasts. Are the
point forecasts significant at the 5% level?





1 LK: Although you were advised on the lectures to run unit root / stationarity tests not only on the level
series but on the first difference as well, to save time you are not expected to do so in this assignment.
You are not expected either to test the residuals from the test regressions in part (c).
4

ECON90033 Semester 2, 2025 Assignment 2
Exercise 3 (17 marks = 2 + 14 + 1)

Launch RStudio, create a new project and script, and name both a2e3. Import the data
from the a2e1.RData file, save it as a2e3.RData, attach it to your R project, and
calculate the daily log returns of the Hang Seng Index (r).

a) Estimate an ARMA(p,q) - GARCH(1,1) model for r taking the p and q parameters
in the mean equation from the best fitting model in Exercise 2.

b) Briefly evaluate the results of the following tests at the 5% significance level:

i. Weighted Ljung-Box tests on the standardized residuals
ii. Weighted Ljung-Box tests on the standardized squared residuals
iii. Weighted ARCH LM tests
iv. Nyblom stability tests
v. Sign bias tests
vi. Adjusted Pearson goodness-of-fit tests
vii. Two-tail t-test on each parameter with zero hypothesized value

c) Are you satisfied with the estimated model? Why or why not?

学霸联盟