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Department of Economics

Spring Semester 2023-2024

ECN602 Applied Macroeconometrics, Spring 2024

Deadline: 12noon Wednesday, 17 April 2024

The completed assignment should be submitted online through Blackboard/Turnitin before 12noon on Wednesday, 17 April 2024. Any unauthorised late submissions after 12noon on the day of the deadline will incur a penalty of 5%. An additional 5% penalty will be added after 24 hours from 12noon on the day of the deadline and then at 24 hour intervals, up to 5 working days late. After that, a mark of zero will be awarded.

Specific Submission Guidelines

❼ The membership of groups is available on the module website. One student from each group (the group representative) must submit the completed assignment through Blackboard/Turnitin. Each group must submit ONLY ONE copy.

❼ Include the module code and your group number on the name of the submitted file (e.g. the submitted file of group number 3 should be marked as “ECN602-Group3”).

❼ You must attach a submission template coversheet to the front of your work when submitting it to Turnitin to avoid a 5% penalty. Full details of this policy can be found in the Student Handbook. The assessment code should be the module code together with your group number (e.g. “ECN602-Group3”) and registration no should include the registration numbers of all group members.

❼ The assignment should be type-written.

❼ In the main part of the assignment, you should include your answers to the three questions and a reference list. This part should be no longer than 2000 words. Please do not alter the formatting (margins, font, font size nor line spacing).

❼ An appendix containing all the tables and figures that you refer to should also be added. Stata tables should be formatted using Courier New font 9. The appendix should be no longer than 8 pages. Note that the appendix is not included in the word limit of 2000 words.

❼ All pages must be numbered. All tables and figures must be labelled and must have self-explanatory titles. All tables and figures should be discussed in the text, so you need to be selective – no marks will be given for tables and figures that are not discussed.

❼ Harvard referencing must be used. For more information see:

https://www.librarydevelopment.group.shef.ac.uk/referencing/harvard.html

❼ The Stata commands used to answer question 2 should be provided at the end of the completed assignment. This is not included in the word limit of 2000 words. Assignments with no Stata commands will be given a zero mark in this question.

❼ The total marks for the assignment are 100. The marks in parentheses ( ) are the marks for each question and the marks in brackets [ ] are the marks for the components of each question.

❼ 10 marks are allocated to the presentation of your assignment. This includes: (i) clear structure and layout; (ii) clarity and logical presentation of findings and arguments; (iii) adherence to page limit and other specifications; (iv) correct use of references.

❼ Please ensure that you have read the assessment guidelines provided in the Student Handbook, including the guidance about submission requirements, extension requests and extenuating circumstances and the use of unfair means.

Questions

1. (15 marks) Suppose that the observed process is yt = εt + θ1εt−1 + θ2εt−2, where εt is a white noise process with zero mean and unit variance. Calculate the autocorrelation coefficients ρk = Corr(yt , yt−k) for k = 0, 1, 2, 3, . . .. Show your work. Show that the process {yt} is stationary.

2. (55 marks) From any (reliable) data source choose a univariate time series of your interest, with at least 50 equally spaced data points. (Choosing a time series that has already been provided to you in this module, either as part of an application in the lectures or for the labs, will incur a penalty of 50% on this question.)

(a) [10 marks] Explain why your chosen time series is of interest and discuss its features (for example, trend, structural breaks, cycle elements). Make sure to cite your data source and any references you may use.

(b) [10 marks] Determine if your time series is stationary or not using the Augmented Dickey Fuller (ADF) test. Explain clearly what you are doing.

(c) [25 marks] Use the Box-Jenkins procedure to obtain the most suitable model for your time series. Explain each step carefully. (Note that if the series is non-stationary, you need to use the appropriate transformation to make it stationary.)

(d) [10 marks] Consider the “best” model you chose in part (c) and perform Engle’s Lagrange Multiplier (LM) test on the residuals to determine whether or not the residuals show conditional heteroscedasticity. Explain clearly what you are doing. (Note that if the series does not exhibit conditional heteroscedasicity, you still need to show and explain the results of the test.)

3. (20 marks) After reading Engle (2001), write a short reflection addressing the following:

❼ What were the key points in the article that you found most interesting, and why?

❼ How could the findings and ideas of the article inform your own future research involving macroeconomic or financial data?

Engle, R.F. (2001). GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics, Journal of Economic Perspectives, 15(4), 157-168.

(The article is available in the Resource List.)

NOTE: 10 marks will be allocated to the presentation of your assignment. This includes:

(i) clear structure and layout; (ii) clarity and logical presentation of findings and arguments; (iii) adherence to page limit and other specifications; (iv) correct use of references.