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 cpitis the natural logarithm of the Consumer Price Index at time t and ∆is the first difference operator,then:a)FollowtheBox-Jenkinsapproach inbuildinganARMA(p,q)modelfor∆cpit;specifically,i.Obtaintheautocorrelationfunction(ACF)andpartialautocorrelationfunction(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 ∆cpitover the sample period 1960Q1to2017Q4.Fromyourestimations,whichisthesuitablemodelorder?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 aTable).[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 datawell?[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 ∆cpitseries and theforecasts that you have generated over the specified out-of-sample period. Comment on theresults.[10%]1
Financial Econometrics
QUESTION 2.Conductallyourstatisticaltestsatthe10% levelfor this question.Support your discussion for this question using appropriate mathematical equations and references in the relevant area(s) ofresearch.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 followingregression:s¥/$,t = α+β₁ptJP+ β₂ptUS, (1)where s¥/$,tis the natural logarithm of the spot exchange rate (the amount of Japanese yen per 1 US dollar) and ptJP and ptUS are the natural logarithms of Japan and US pricelevels 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%]2
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 theseries.[5%]
c)Describe the ARCH-GARCH family of models and explain why it may be useful in explaining the volatility of WTIreturns.[10%]d)UsetwounivariateGARCHtypemodelswhichnestARCH(e.g.GARCH,PGARCH,etc.) to estimate the volatility of returns, explaining the motivation for their use. Test for the differencesbetweenthemodels(e.g.parametersignificanceand Likelihood Ratio (LR)tests),anddiscusshow their volatility estimates and residualsdiffer.
