Econometrics report
Tasks:
Download the Excel files. Each of you will have a different set of data. Sheet 1 contains the monthly inflation rates of eleven countries. Sheet 2 the monthly historical price of S&P500 and other indices. Sheet 3 contains daily stock prices of eleven US companies, SMB and HML risk factor and US risk free rate. Note: all the Fama-French data are in percentages. Sheet 4 contains USD/GBP spot and forward exchange rates. All data are obtained from Eikon Refinitiv and Kenneth French’s website, which can be access here:
Each of you will be assigned one company, one index and the number of lags for VAR in question 5.
1. Employ the Box-Jenkins approach, identify the ARMA form of the assigned inflation rates following the steps below:
a. Plot the correlogram of the time series.
(2 marks)
b. From the correlogram, propose three models AR, MA or ARMA that could potentially be suitable for this time series. Provide justification for the choices.
(10 marks)
c. Estimate all of the proposed and compare their Akaike Information Criteria to identify the most suitable model for the assigned inflation rate.(15 marks)
2.a. Apply the Fama-French 3-factor model on the log return your assigned US company. The Fama-French 3-factor model has the following form:
(1)b. models (10 marks)
Report your estimation results and comment on the significance levels of the estimated coefficients. Comment on the meaning and significance of all the factors.
c. Is Fama-French a good model for the particular stock? Explain your answer with evidence from your computation.(5 marks)
3. Conduct the ARCH-LM test on the residuals of the estimation of model (1) in question 2. Report and comment on the result of the test.(5 marks)
4.a. Estimate the Fama-French 3-factor model with GARCH(1,1) on the company stock return. Comment on the estimated result regarding the magnitude and significance of the model.(10 marks)
b. Discuss if introducing GARCH(1,1) for this model is appropriate.
(5 marks)
5. Apply a bivariate VAR model to the monthly log return on S&P500 and the monthly log return on your given index.
a. Report the optimal lag-length table. What are the optimal lag lengths according to different criteria?
