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N1611 Financial Econometrics

2022-23

Coursework Guidelines

· This coursework is worth 70% of the overall assessment of the module.

· The coursework consists of understanding theoretical models, along with data manipulation, analysis and interpretation. Please note that this is NOT a group exercise. Although you may discuss the project with others, the coursework analysis and discussion must be worked out and written up individually. You may receive reduced or no marks if there are strong similarities between the work handed in by two or more people.

· This coursework consists of TWO questions. Candidates should attempt ALL questions.

· Your answer to each question should INCLUDE the full references of the articles, books and other sources cited. You can present the references at the end of your answer and discussion to each question.

· Information on where to find material: The material to be used to answer the questions is on the Canvas site. However, students are expected to do their own research and add different sources.

· STATA output should NOT be copied and pasted directly into the project. You should present your results (e.g. regression/model output) as it would appear in published academic research papers. (Look at some papers --sometimes the output is in Tables, sometimes presented as estimated equations with s.e./t-statistics/p-values in brackets under the corresponding coefficient, together with appropriate diagnostic statistics and their p-values).

· You should always comment on your estimation results, i.e. what is the intuition behind your empirical findings.

· For question 2(d), the univariate GARCH type models covered in the module will primarily be required to estimate the volatility.

· The word count of the project must be printed on the first page of the coursework. The maximum word count is 2000, e.g., you could split this word count across the questions. The tables, references and appendices are not included in the word count.

· Note that your coursework is to be submitted electronically via Canvas. Please check for the deadline of submitting your work on Canvas module site (under "Assignments" section). For more information regarding the deadline or issues on submitting your work, please check with the UG School office (at this email: [email protected]).

· Upload your word (or pdf) document through the "E-submissions" link on the module’s Canvas site by the deadline. There is no need to upload or submit the data estimation file.

· Late submissions will be treated according to university regulations. More information on assessment regulations can be found here:

http://www.sussex.ac.uk/adqe/standards/examsandassessment/esubmission

Question 1

You are given the monthly time series of the interest rates paid on three-month, three-year, and seven-year US government securities for the period of January 1997-April 2021. The data file label is "RATES.xls", uploaded on Canvas along this file. The variables in the file are labelled TBILL, R3 and R7, respectively.

a) Explain the concepts of non-stationarity and cointegration, and how are they connected. Illustrate how one can test for cointegration using the two-step Engle and Granger approach.     [15%]

a) Test the variables to show that the rates all act as unit root processes.  [5%]

b) Test for the long-run relationship using the two-step Engle and Granger cointegration approach applied to the following regression:

                   TBILL_,t = α+β₁R3_t + β₂R7_t.                              (1)    [15%]

c) After determining whether Equation (1) is a cointegrating relationship or not, estimate the respective Error Correction Model (ECM). Perform appropriate diagnostic tests on the estimated ECM. Comment on your results.        [15%]

Conduct all your statistical tests at the 5% level for this question. Perform unit root tests by using the maximum lag length of 8 lags, explaining your approach for selecting the appropriate lag order for each test. Support your discussion for this question using appropriate mathematical equations and references in the relevant area(s) of research.

Question 2

You are given the weekly (Wednesday to Wednesday) closing prices of the FTSE 100 stock market index, labelled FTSE100, covering the period 02 January 1991 to 30 September 2020. The data file name is "FTSE100.xls", uploaded on Canvas along this file:

a) Discuss the statistical properties of the series by (i) calculating relevant summary statistics of the FTSE 100 returns (also known as log price changes), and (ii) plotting the returns, as well as their histograms and quantile-quantile (QQ) diagrams.       [5%]

b) Plot the ACF for returns, squared returns, and absolute returns, then discuss whether any of these plots provide an indication about the predictability of the series.    [10%]

c) Describe the ARCH-GARCH family of models and explain why it is useful in explaining the volatility of financial returns.    [15%]

d) Use three univariate GARCH type models which nest ARCH (e.g. GARCH, PGARCH, etc.) to estimate the volatility of FTSE 100 returns, explaining the motivation for their use. Test for the differences between the models (e.g. parameter significance and Likelihood Ratio (LR) tests), and discuss how their volatility estimates and residuals differ. Finally, comment on the behaviour of estimated conditional variances from your models.         [20%]

Conduct all your statistical tests at the 5% level for this question. Support your discussion for this question using appropriate mathematical equations and references in the relevant area(s) of research.