ECON1195 Financial Econometrics
Assignment 2
August 2022
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 11.59 pm (Melbourne
time) Sunday, 2 October 2022. Answers can be typed or handwritten and
scanned. You also need include relevant results/graphs from R in your answers
and 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%.
1
Question 1
Let rt denotes the return of a financial asset and σt denotes the standard
deviation of returns at time t. Suppose rt follows rt = μ + et with et = ztσt
where zt ～ N(0, 1).
(a) Write down an ARCH(q) model with q=3 for σ2t .
(b) Write down an GARCH(q,p) model with q=1 and p=2 for σ2t .
(c) Derive the unconditional variances of the ARCH model in (a) (show all
necessary steps).
(d) Derive the unconditional variances of the GARCH model in (b) (show
all necessary steps).
(e) Discuss and compare the two ARCH-type models in (a) and (b).
Question 2
The goal of this question is to conduct an empirical analysis using real data.
This question will be marked on the quality of your write-up, presentation and
analysis. Keep the explanations succinct, detailing only essential information
(no more than 350 words).
The dataset ’INDPRO.csv’ contains the US industrial production index (IN-
DPRO) - a very important macroeconomic indicator which measures the real
production output of manufacturing, mining, electric and gas utilities. As a
macroeconomist in the bank, you are required to write a short report in answer-
ing the following tasks:
1. Provide useful preliminary analysis of continuously compounded re-
turns of INDPRO;
2. Use appropriate steps to decide what type of models (ARMA or ARIMA)
should be used to fit for the continuously compounded returns of IND-
PRO; (Week 5/6 materials)
3. Use appropriate steps to analyse and model the volatility of the con-
tinuously compounded returns of INDPRO. (Week 7/8 materials)
4. Give a conclusion about your choice of model.