Explain the conceptsof non-stationarity and cointegration, and how are they connected.

N1611Financial Econometrics –Coursework2020-21Coursework GuidelinesThe assessment for N1611 Financial Econometrics module is by this coursework, hence this coursework is worth 100% of the overall assessment of the module.The coursework consists of understanding of 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 THREE 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 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).You should always comment on your estimation results, i.e. what is the intuition behind your empirical findings.For question 3(d), the univariate GARCH type models covered in the module will 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 countis 2500 (with+/-10%of this word count), 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 deadlineof submitting your work on Canvas module site (under “Assignments” section).

Question 1You are given quarterly data ofU.S. House Price Index (HPI) over the period 1975Q1 to 2019Q4. The data file name is “HousePrice.xls”. Calculate the logarithmic change of the price series, i.e.,∆hpit=hpit-hpit-1, wherehpitis the natural logarithm of the House Price Index at time tand∆is the first difference operator, then:a)Follow the Box-Jenkins approachin building an ARMA(p,q)model for ∆hpit; specifically,i)

Obtain the autocorrelation function (ACF) and partial autocorrelation function (PACF) for ∆hpit(specify the number of lagsto be 8) using data from 1975Q1 to 2017Q4 (Note that this is not the full sample).

Discuss the significance of the ACF and PACF coefficients andidentify the suitablemodels that you wouldestimate.[5%]ii)Estimate all ARMA models from order (0,0) to (4,4) for ∆hpitover the sample period 1975Q1 to 2017Q4.

From your estimations, which is the suitablemodel 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 suitablemodel(s) from Question a(ii). Again, use only the sample 1975Q1 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 datawell?[10%]b)Use the model(s) estimated in Question a(iii)to generate one step ahead (static) forecasts for the period 2018Q1 -2019Q4.

Create a graph of the actual ∆hpitseries and the forecasts that you have generated over the specified out-of-sample period. Comment on the results.[10%]Conduct all your statistical tests at the 5% level for this question.Question 2You are given the monthly time series of the spot British pound exchange rate against the US dollar (denoted as GBPtoUSD) and the Consumer Price Indices, which proxy the general price levels, for the UK and the US (denoted respectivelyas UKCPI and USCPI)for the period of January 1991-August 2020. The data file name is “PPP.xls”:a

)Explain the conceptsof 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 forlong-run Purchasing Power Parity (PPP) using the two-step Engle and Granger cointegration approach applied tothe following regression:s£/$,t1ptUK2ptUS, # (1)
where s£/$,tis the natural logarithm of the spot exchange rate (the amount of British pound per 1 US dollar) andptUKand ptUSare the natural logarithms of the UK and US price levels respectively. Under the long-run PPP,β1=1andβ2=-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%]Conduct all your statistical tests at the 10% level for this question. Support your discussion for this question using appropriate mathematicalequations and references in the relevant area(s) of research.

Question 3You are given the daily closing prices of three stock market indices, namely the S&P 500, the FTSE 100, and the NIKKEI 225, covering the period 01 January 1991-30 September 2020.

Discuss the statistical properties of these series by (i) calculating relevant summary statistics of the returns, 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 thepredictability of these series.[5%]c)Describe the ARCH-GARCH family of modelsand explain why it is useful in explaining the volatility of stock market returns.[10%]d)Use threeunivariate 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.[15%]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