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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%]
b)Test the variables to show that the rates all act as unit root processes.
[5%]
c)Test for the long-run relationship using the two-step Engle and Granger cointegration approach applied to the following regression:

TBILL,t = α+β?R3t_x005f_x001f__x005f_x005f _x001f__x001f_ + β?R7t . (1)

[15%]
d)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.