- Explain what is meant by stationarity, unit roots, and cointegration. Explain how these concepts are related to one another. Apply appropriate pre-testing and then implement the Engle-Granger two-step procedure to model the relationship between the log of real consumers’ expenditure (let this be your dependent variable) and the log of real GDP (let this be your independent variable) for the USA using the ‘ustrix.dta’ STATA dataset. This dataset is available on the Canvas site for the module. Now estimate an unrestricted error correction mechanism (ECM) model containing these variables. Interpret and compare the short-run effects, long-run effects and the speed of adjustment in these two models. What is the evidence of cointegration across the two models? Which of these two models do you prefer and why? Explain your choice.
- What are ARCH effects and what are the econometric consequences if these effects are ignored in modelling? Provide an example drawn from financial economics and explain why it may exhibit ARCH effects. Estimate a CAPM relationship between the return to Facebook stock and the S&P500 series using the entire ‘facebook.dta’ STATA dataset from the module’s Canvas site. Choose a range of appropriate econometric tools to test for the presence of ARCH effects in this relationship. Interpret and explain your results. What do you conclude? Does the estimated market beta change if you account for volatility clustering? Explain your answer. Discuss whether or not this is in line with your expectations. Assess empirically whether there is any evidence that negative shocks to Facebook returns have a differential effect on volatility compared to positive ones.