SEMESTER 2 2022/23
GROUP COURSEWORK BRIEF:
Quantitative Research in Finance Dr Renatas Kizys
Module Code:
Assessment:
Group Coursework
Weighting:
Module Title:
Module Leader:
Submission Due Date: @ 16:00
19th May 2023
Word Count/Duration:
Method of Submission:
Electronic via Blackboard Turnitin ONLY (You are not required to submit a hard copy) (Please ensure that your name does not appear on any part of your work)
Any work submitted after 16:00 on the deadline date will be subject to the standard University late penalties (see below), unless an extension has been granted, in writing by the Senior Tutor, in advance of the deadline.
University Working Days Late:
More than 5
(final agreed mark) * 0.9 (final agreed mark) * 0.8 (final agreed mark) * 0.7 (final agreed mark) * 0.6 (final agreed mark) * 0.5 0
This assessment relates to the following module learning outcomes:
A. Knowledge and Understanding
A1. Demonstrate a critical understanding of the basic theory of financial econometrics;
A2. Demonstrate a critical understanding of some specific applications of such theory;
A3. Apply such understanding to a specific empirical project;
A4. Demonstrate competence in using a basic econometrics software package.
B. Subject Specific Intellectual and Research Skills B1. Demonstrate quantitative skills in evaluating numerical data. C. Transferable and Generic Skills C1. Demonstrate skills in utilizing analysis software.
Group Coursework Brief:
You should be aware that all members of your group share responsibility for any academic integrity breaches or other issues that may arise from your group’s coursework submission. The awarded mark to a group implies that each member of that GROUP receives the same mark as others in the same group. Use STATA for estimations and tests. Assume, where relevant the significance level of 5%. PLEASE NOTE THAT ONLY ONE MEMBER OF THE GROUP SHOULD SUBMIT THE ASSIGNMENT TO BLACKBOARD TURNITIN.
Answer ALL Questions in Full
Question ONE
Question ONE requires using the data from the module page on Blackboard. The data file Q1.XLS contains the short-term interest rates for selected OECD countries, the US policy interest rate (i.e., effective federal funds rate) (USinterest), the US VIX volatility index (VIX), and the US economic policy uncertainty index (EPU). These data are obtained from the OECD database and the Federal Reserve Bank St Louis’ database.
Suppose that you want to study the (spillover) effect of US monetary policy on the short-term interest rates in the OECD countries. To this end, consider the following regression model:
𝑅 =𝛼+𝛽𝑅𝑈𝑆+𝑢 , (1) 𝑖,𝑡 1𝑡 𝑖,𝑡
Code Help, Add WeChat: cstutorcs
SEMESTER 2 2022/23
where 𝑅 is the short-term interest rate for an OECD country 𝑖 (each group will be allocated a country), 𝑅𝑈𝑆
is the US policy interest rate, and 𝑢𝑖,𝑡 is the random disturbance term.
IMPORTANT NOTE: You MUST answer each part of the question separately and clearly.
Required for Question ONE
a) What assumptions would you make on the random disturbance term and/or the explanatory variable so that the estimated coefficients are BLUE? Do you expect these assumptions to hold for the model outlined in Equation (1)? Discuss.
b) Estimate Equation 1 using OLS. Summarise the goodness of fit of the model and test the hypothesis that the short-term interest rate in the selected country responds positively to the US policy interest rate. Outline the null and alternative hypotheses for this test. Perform the test and comment on the result.
c) Perform a test for heteroscedasticity in the residuals from Equation (1). Comment on the result. What inferences would you make in the presence of heteroscedasticity? What methods would you employ to remedy the presence of heteroscedasticity?
d) Perform a test for serial correlation in the residuals from Equation (1). Comment on the result. What inferences would you make in the presence of serial correlation? What methods would you employ to remedy the presence of serial correlation?
e) In addition to the monetary policy, it is believed that uncertainty is another important factor in explaining the short-term interest rate. Suppose that there are two types of uncertainty under your consideration, economic policy uncertainty (EPU) (measured by the US economic policy uncertainty index) and financial uncertainty (VIX) (measured by the VIX volatility index). Consider the following regression model:
𝑅 =𝛼+𝛽𝑅𝑈𝑆+𝛽𝑈𝑈𝑆+𝑢 , (2A,B) 𝑖,𝑡 1𝑡 2𝑡 𝑖,𝑡
where 𝑈𝑈𝑆 is the uncertainty index measured by either VIX or EPU. Perform OLS estimations of Equation 𝑡
(2A,B) twice. Use VIX to measure 𝑈𝑈𝑆 in Equation 2A and use EPU in in Equation 2B. Compare your results 𝑡
across the three specifications (Equations 1, 2A and 2B). Which regression specification should be employed? Which uncertainty measure (VIX or EPU) should be included in the regression model?
[50 marks] [Maximum 1000 words]
Question TWO
Question TWO requires to use the same data file as for Question ONE. Required for Question TWO a) Depict the short-term interest rate, 𝑅𝑖,𝑡, on a time series graph. Comment on the result.
b) Perform a unit root test on the interest rate. Is the variable I(0) or I(1)? Carefully outline the test equation, as well as the null and alternative hypotheses for this test. Discuss if an intercept and/or linear trend need to be included in the test equation.
Code Help
SEMESTER 2 2022/23
If the interest rate is I(1), for the remainder of this question transform it into FIRST DIFFERENCES. If the interest rate is found I(0) no transformation is necessary; continue using the variable in LEVELS.
c) Estimate the autocorrelation and partial autocorrelation functions for the interest rate (in LEVELS or DIFFERENCES, depending on part b). Comment on the estimation output.
d) Estimate AR(p) models with p=1,2,3, and ARMA(p,q) models with p=1,2,3 and q=1,2,3. Summarise in tables the coefficient estimates, the estimated standard errors, the information criteria AIC and BIC, as well as the Ljung-Box Q test for the first 12 autocorrelations in the residual series. Comment on the results.
e) Based on the estimation output in d), select the optimal time-series model. Justify your choice.
[25 marks] [Maximum 500 words]
Question THREE
Question THREE requires to use the same data file as for Question ONE. Required for Question THREE
If the interest rate is I(1), for the remainder of this question transform it into FIRST DIFFERENCES. If the interest rate is found I(0) no transformation is necessary; continue using the variable in LEVELS.
a) Depict 𝑅𝑖,𝑡 on a time series graph and discuss if there is evidence of volatility clustering in the data. Comment on the result. Calculate the squared 𝑅𝑖,𝑡 and depict graphically the correlation and partial correlation functions of the squared 𝑅𝑖,𝑡. Comment on the result.
b) With respect to the series 𝑅𝑖,𝑡, test for the presence of conditional heteroscedasticity in the residuals of the conditional mean model, formulated as in Equation (1). Perform the LM-ARCH test for lag orders 1 and 6. Comment on the results. Is there evidence of conditional heteroscedasticity in the residuals? Please use the same conditional mean model in c) and d) below.
c) Proceed to estimate ARCH(p) models with p=1,…,6. Summarise the estimated models in a table. Discuss the results. Which of the estimated models provides the best fit? The conditional mean model is as in b).
d) Now estimate the conditional variance using GARCH(1,1) and TGARCH(1,1) models. Discuss the results. Which of the two models provides the best fit? The conditional mean model is as in b).
e) Now estimate a GARCH(1,1)-M model, in which the conditional mean model is formulated as 𝑅𝑖,𝑡 = 𝛼 +
𝛽 𝑅𝑈𝑆 + Λ𝜎2 + 𝑢 . Comment on the results. 1𝑡 𝑖,𝑡−1 𝑖,𝑡
[25 marks] [Maximum 500 words]
Programming Help, Add QQ: 749389476
SEMESTER 2 2022/23
Nature of Assessment: This is a SUMMATIVE ASSESSMENT. See ‘Weighting’ section above for the percentage that this assignment counts towards your final module mark.
Word Limit: +/-10% either side of the word count (see above) is deemed to be acceptable. Any text that exceeds an additional 10% will not attract any marks. The relevant word count includes items such as cover page, executive summary, title page, table of contents, tables, figures, in-text citations and section headings, if used. The relevant word count excludes your list of references and any appendices at the end of your coursework submission.
You should always include the word count (from Microsoft Word, not Turnitin), at the end of your coursework submission, before your list of references.
Title/Cover Page: You must include a title/ cover page that includes: your Student ID, Module Code, Assignment Title, Word Count. This assignment will be marked anonymously, please ensure that your name does not appear on any part of your assignment.
References: You should use the Harvard style to reference your assignment. The library provide guidance on how to reference in the Harvard style and this is available from: http://library.soton.ac.uk/sash/referencing
Submission Deadline: Please note that the submission deadline for Southampton Business School is 16.00 for ALL assessments.
Turnitin Submission: The assignment MUST be submitted electronically via Turnitin, which is accessed via the individual module on Blackboard. Further guidance on submitting assignments is available on the Blackboard support pages.
It is important that you allow enough time prior to the submission deadline to ensure your submission is processed on time as all late submissions are subject to a late penalty. We would recommend you allow 30 minutes to upload your work and check the submission has been processed and is correct. Please make sure you submit to the correct assignment link.
Email submission receipts are not currently supported with Turnitin Feedback Studio LTI integrations, however following a submission, students are presented with a banner within their assignment dashboard that provides a link to download a submission receipt. You can also access your assignment dashboard at any time to download a copy of the submission receipt using the receipt icon. It is vital that you make a note of your Submission ID (Digital Receipt Number). This is a unique receipt number for your submission, and is proof of successful submission. You may be required to provide this number at a later date. We recommend that you take a screenshot of this page, or note the number down on a piece of paper.
The last submission prior to the deadline will be treated as the final submission and will be the copy that is assessed by the marker.
It is your responsibility to ensure that the version received by the deadline is the final version, resubmissions after the deadline will not be accepted in any circumstances.
Important: If you have any problems during the submission process you should contact ServiceLine immediately by email at or by phone on +44 (0)23 8059 5656.
Late Penalties: Further information on penalties for work submitted after the deadline can be found here.
Special Considerations: If you believe that illness or other circumstances have adversely affected your academic performance, information regarding the regulations governing Special Considerations can be accessed via the Calendar: http://www.calendar.soton.ac.uk/sectionIV/special-considerations.html
SEMESTER 2 2022/23
Extension Requests: : Extension requests along with supporting evidence should be submitted to the Student Office as soon as possible before the submission date. Information regarding the regulations governing extension requests can be accessed via the Calendar: http://www.calendar.soton.ac.uk/sectionIV/special-considerations.html
Academic Integrity Policy: Please note that you can access Academic Integrity Guidance for Students via the Quality Handbook: http://www.southampton.ac.uk/quality/assessment/academic_integrity.page?. Please note any suspected cases of Academic Integrity will be notified to the Academic Integrity Officer for investigation.
Feedback: Southampton Business School is committed to providing feedback within 4 weeks (University working days). Once the marks are released and you have received your feedback, you can meet with your Module Leader / Module Lecturer / Personal Academic Tutor to discuss the feedback within 4 weeks from the release of marks date. Any additional arrangements for feedback are listed in the Module Profile.
Student Support: Study skills and language support for Southampton Business School students is available at: http://www.sbsaob.soton.ac.uk/study-skills-and-language-support/.
External Examiner:
External Examiner Comments:
Final Approval by External Examiner Date:
Module Leader Response to External Examiner:
(Please note these comments are REQUIRED and will be sent to the External Examiner)