Obtain the VIX index from 2012-01-01 to 2017-02-01. Focus on the series of the daily closing index. Compute the monthly log return rt of the VIX index. (you can use the function monthlyReturn). getSymbols("^VIX",from=2012-01-01,to=2017-02-01,src="yahoo")

(1) Using the command ar to identify an AR mdoel for rt . Perform estimation and write down the fitted model, including residual standard deviation.

(2) Make an ACF plot. Propose and fit an MA model based on the ACF plot. Perform estimation and write down the fitted model, including residual standard deviation. Are all the MA coefficient significant? Is the fitted model invertible? (check the roots of the MA polynomial) Make a tsdiag plot for the model. Judging from the plots, is the fitted model adequate? 1

(3) Make a PACF plot. Propose and fit an AR model based on the PACF plot. Perform estimation and write down the fitted model, including residual standard deviation. Are all the AR coefficient significant. Is the fitted model stationary? (check the roots of the AR polynomial) Make a tsdiag plot for the model. Judging from the plots, is the fitted model adequate?

(4) Based only on the AIC values of the two models in (2) and (3), which model is better?