Question 2 (100 marks) Consider the following moving average process, MA(3): where a, is a white noise process, with E(w, )=0, var(u, )=o' and " ISA 0=('n"n )ADD a) Derive the mean, E(Y, ), the variance, var(Y, ), and the covariances cov( Y,, Y,_,), cov(Yt, Yt-2), cov(Yt, Yt-3) of this process. b) Give a definition of a (weakly) stationary time series process. Is the MA(3) process (weakly) stationary? Explain your answer in detail. c) What are the features of the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) of a MA(3) process? What are the features of the ACF and PACF of an AR(3) process? Why are the ACF and PACF relevant when working with time series data?Question 3 (100 marks) Consider the following model Y, = B + BX, +u, Where the error term follows an autoregressive process AR(1) where -1