1. Let (Xt : te Z) be a causal AR(2) process, Xt = 1Xt-1+ 12Xt-2+ wt, wt ~WN(0, q?). Determine the two-step-ahead Best Linear Predictor of the process, i.e. X,+2 by finding X+2 such that E[(Xn+2 - X"+ 2) Xk] = 0, k = 1, 2, . .., n. 2. Let It represent the cardiovascular mortality series (cmort available in the R package "astsa"). (a) Plot the sample acf and pacf of It and determine an appropriate ARMA model for the data. (b) Fit the model to the data by using the function sarima in R package astsa and then determine the fitted model. (c) Use the fitted model to find the 1, . . ., 4-step-ahead prediction of the series, i.e. Int, k = 1, 2, 3, 4, and compare your computation with the one obtained by applying the R function sarima. for. Please show the details of your computations. (d) Compute 'n+1, In+2, and PR In+3 and compare it with the one produced by sarima. for. Please show the details of you computations. (e) Fit an appropriate AR model to It using linear regression. Hint: Use the R function ar . ols. (f) Find the forecasts over a four week horizon, i.e. In, k = 1, 2,3,4. Compare your results with those obtained in part (c)