Consider the following MA(3) time series process: v, = 5+a,-0.5a,_, +0.25a,_2 -0.la,-3, where fat} is a Gaussian white noise series with mean zero and constant variance o'=0.025. a) Derive the formula for the lag-1 autocorrelation for the time series v, like we did in class. You can use for a model, the computations for the MA(2) series from the lectures. b) Use your formula to calculate the lag-1 autocorrelation for vi? c) Use the code from the class in BuildingSeries.R to build a realization of this MA(3) process of 1000 time periods (use an initial value of 0 like we did). Then calculate the mean and first two autocorrelations. How closely do they match your theoretical calculations