1. Given an AR(2) model X 4 = 0.8X+-1-0.15X4-2+W7, where we are Gaussian white noises from N(0,02). (1) Using the iterative form (page 14 of lecture 4) of the covariance function for AR(p) model to compute y(0) to y(4). (2) Is the AR(2) model is stationary. Why and why not? 2. Obtain the VIX index from 2015-01-01 to 2020-02-01. 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='2015-01-01', to='2020-02-01',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? 1. Given an AR(2) model X 4 = 0.8X+-1-0.15X4-2+W7, where we are Gaussian white noises from N(0,02). (1) Using the iterative form (page 14 of lecture 4) of the covariance function for AR(p) model to compute y(0) to y(4). (2) Is the AR(2) model is stationary. Why and why not? 2. Obtain the VIX index from 2015-01-01 to 2020-02-01. 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='2015-01-01', to='2020-02-01',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