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N1611 Financial Econometrics – Coursework #2

2023-24

Coursework Guidelines

· This coursework is worth 70% of the total mark for the module.

· The coursework consists of understanding theoretical models, along with data manipulation, analysis and interpretation. Please note that this is NOT a group assignment. Although you may discuss the project with others, the analysis and discussion of the coursework must be done and written individually. You may receive a reduced mark or no mark if there are strong similarities between the work submitted 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 may provide the references at the end of your answer and discussion for each question.

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

· STATA output should NOT be copied and pasted directly into the project. You should present your results (e.g., regression/model output) as they would appear in published academic research papers. (Take a look at some papers --sometimes the output is presented in Tables, sometimes presented as estimated equations with s.e./t-statistics/p-values in parentheses 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 GARCH models, the univariate GARCH type models covered in the module can be used primarily to estimate 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., this word count could be split across the questions. Tables, references and appendices are not included in the word count.

· Note that your coursework must be submitted electronically via Canvas. Please check the deadline for submitting your work on the Canvas module site (under "Assignments" section). For more information regarding the deadline or questions about submitting your work, please contact the UG School Office (at this email: [email protected]).

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

· Late submissions will be handled in accordance with university policy. For more information on assessment policies, please see:

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

Question 1

You are given the monthly time series of the spot Japanese yen exchange rate against the US dollar (denoted as JPYtoUSD) and the Consumer Price Indices, which proxy the general price levels, for Japan and the US (denoted respectively as JPCPI and USCPI) for the period of January 1991-August 2020. The data file name is "PPP.xls", which is uploaded to Canvas along with this file.

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

a) Test for long-run Purchasing Power Parity (PPP) using the two-step Engle and Granger cointegration approach applied to the following regression:

    s_JPY/USD,t = α+β₁p_t^JP + β₂p_t^US,                                                         (1)

where s_JPY/USD,t is the natural logarithm of the spot exchange rate (the amount of Japanese yen per 1 US dollar) and p_t^JP and p_t^US are the natural logarithms of Japan and US price levels respectively. Under the long-run PPP, β₁ =1 and β₂ =-1.       [20%]

b) Estimate the respective Error Correction Model (ECM) if Equation (1) is a cointegrating relationship. Perform appropriate diagnostic tests on the estimated ECM. Comment on your results.     [15%]

Notes: (i) Perform unit root and cointegration tests by using the maximum lag length of 8 lags, explaining your approach to selecting the appropriate lag order for each test, (ii) If Equation (1) is not a cointegrating relationship, question c) may be answered by estimating an alternative appropriate model to estimate the short-run dynamics among variables, and (iii) Support your discussion of this question with appropriate mathematical equations and references in the relevant area(s) of research.

Question 2

You are given the weekly (mid-week) spot prices of WTI crude oil (dollars per barrel), namely WTI, for the period from January 06, 2010 to October 25, 2023. The data file name is "WTI.xls", which is uploaded to Canvas along with this file.

a) Discuss the statistical properties of the series by (i) calculating relevant summary statistics of the WTI log 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, returns squared, and absolute returns, and then discuss whether any of these plots provide an indication of the predictability of the series.    [10%]

c) Describe the ARCH-GARCH family of models and explain why they are useful in explaining the volatility of WTI returns.     [15%]

d) Build three univariate GARCH-type models which nest ARCH (e.g., GARCH, PGARCH, etc.) to estimate the volatility of returns, explaining the motivation for their use. Test for the differences between the models (e.g., parameter significance and LR tests), and discuss how their volatility estimates and residuals differ.       [20%]

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