Financial Econometrics
Assessment Period: August 2021 (A3)
Submission date: As per directions on your Timetable
Candidates should attempt ALL THREE questions.
GUIDELINES 1. 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.
2. 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.
3. Information on where to find material: Most material that can be used to answer the questions is on the Canvas site. However, students are expected to do their own research and add different sources.
4. STATA output should NOT be copied and pasted directly into the project answer document. You should present your results (e.g. regression 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 stats/p-values in brackets under the corresponding coefficient, together with appropriate diagnostic statistics and their p- values).
5. You should always comment on your estimation results, i.e. what is the intuition behind your empirical findings.
6. For question 3(d), the univariate GARCH type models covered in the module will be required to estimate the volatility.
7. The word count of the project must be printed on the first page of the coursework. The maximum word count is 2500 (with +/-10% of this word count). The tables, references and appendices are not included in the word count.
Financial Econometrics
QUESTION 1. Conduct all your statistical tests at the 5% level for this question.
You are given the quarterly data of U.K. Consumer Price Index (CPI) over the period 1960Q1 to 2019Q2. The data file name is “CPI.xls”. Calculate the logarithmic change of the price series, i.e., ∆cpit= cpit – cpit-1, where cpit is the natural logarithm of the Consumer Price Index at time t and ∆ is the first difference operator, then: a) Follow the Box-Jenkins approach in building an ARMA(p,q) model for ∆cpit; specifically, i. Obtain the autocorrelation function (ACF) and partial autocorrelation function (PACF) for ∆cpit (specify the number of lags to be 8) using data from 1960Q1 to 2017Q4 (Note that this is not the full sample). Discuss the significance of the ACF and PACF coefficients and identify the suitable models that may be appropriate for this time series. [5%]
ii. Estimate all ARMA models from order (0, 0) to (4, 4) for ∆cpit over the sample period 1960Q1 to 2017Q4. From your estimations, which is the suitable model order? Explain why? (You would also need to report all relevant information for the models you estimate, including the value of the AIC and SBIC and other relevant required criteria in a Table). [10%]
iii. Re-estimate the suitable model(s) from Question a(ii). Again, use only the sample 1960Q1 to 2017Q4. Report and comment on the results. Perform diagnostic checks on the residuals from these estimated model(s). Do the model(s) fit the data well? [10%]
b) Use the model(s) estimated in Question a(iii) to generate one step ahead (static) forecasts for the period 2018Q1 – 2019Q2. Create a graph of the actual ∆cpit series and the forecasts that you have generated over the specified out-of-sample period. Comment on the results. [10%]
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Financial Econometrics
QUESTION 2. Conduct all your statistical tests at the 10% level for this question. Support your discussion for this question using appropriate mathematical equations and references in the relevant area(s) of research. 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”: 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. [10%]
b) Test for long-run Purchasing Power Parity (PPP) using the two-step Engle and Granger cointegration approach applied to the following regression:
s¥/$,t = α+β₁ptJP + β₂ptUS, (1)
where s¥/$,t is the natural logarithm of the spot exchange rate (the amount of Japanese yen per 1 US dollar) and pt JP and pt US are the natural logarithms of Japan and US price levels respectively. Under the long-run PPP, β₁=1 and β₂ = -1. [10%]
c) After determining whether Equation (1) is a cointegrating relationship or not, estimate the respective Error Correction Model (ECM). Comment on your results. [10%]
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Financial Econometrics
QUESTION 3. 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. You are given the daily prices of WTI Crude Oil Spot (Dollars per Barrel), namely WTI, covering the period 01 January 1991-23 October 2020. The data file name is “WTI.xls”: a) Discuss the statistical properties of the series by (i) calculating relevant summary statistics of the WTI 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, then discuss whether any of these plots provide an indication about the predictability of the series. [5%]
c) Describe the ARCH-GARCH family of models and explain why it may be useful in explaining the volatility of WTI returns. [10%]
d) Use two 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 Likelihood Ratio (LR) tests), and discuss how their volatility estimates and residuals differ.
