Historical Spot Oil Price Series - Unit Root - The Engel-Granger Approach - Statistics Assignment Help

Assignment Task:

Question 1 (6 marks)

The file oil.dta contains historical spot oil price series (WTI and Brent) at monthly frequency from January 2001 to December 2018 (216 observations). Use the data in the file to answer this question. Let lbrent=log(Brent) and lwti=log(WTI).

(1) Define d=lbrent – lwti (i.e. d is the difference of the two log oil price series) and draw a timeline d. Test if d contains a unit root with “dfgls.” Justify the specification (such as the mean/trend function & the lag selection) implemented for the test. Comment on the results.

(2) Use the Engel-Granger approach to test if lbrent and lwti are cointegrated. Specify the cointegration test up to 2 lags (i.e. three specifications: no lag, 1 lag, and 2 lags). Comment on the results.

(3) Generate dlbrent=d.lbrent (dlbtrent is the first difference of lbrent) and dlwti=d.lwti. Estimate two models -- AR(1) & AR(2) -- for dlbrent and dlwti, respectively. Which one of the two models is with a better specification in each case? Justify.

Question 2 (6 marks)

Use the data set apple.dta for this question. The dataset contains the daily stock return of Apple (aapl) for 2 years, 2017-2018).

(1) Decompose aapl to be the product of sign and its absolute value (i.e. aapl=sgn(aapl)*abs(aapl) where sgn(aapl)=1 if aapl>=0 and -1 if aapl<0). Obtain the autocorrelation function of aapl, sgn(aapl), and abs(aapl) up to 30 lags. Comment on the results.

(2) Estimate two GARCH models for aapl: GARCH(1,1) and GJR ThresholdGARCH(1,1), assuming a “t” distribution in both cases. Comment on the results. Specifically, discuss if the impact of shocks (news) to volatility is asymmetric.

(3) Build ARCH-in-Means models using the specification given in part (2). Comment on the results. Specifically, discuss the risk premium implied by the estimated models.

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