; 1. Consider the MA(2) process xwe + wt-1+ we-2, where we is a white noise process

 

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1. Consider the MA(2) process xwe + wt-1+ we-2, where we is a white noise process with mean O and variance 1. (a) Find the ACVF for xt. (b) Find the predictors x and x. (c) Suppose that we wish to predict 2 from 1 and 23. Find the best predictor of x2 of the form 2 = a1x1 + a3x3, where a and a3 are constants. (d) Suppose that we wish to predict 23 from 21 and 5. Find the best predictor of x3 of the form 3 = a1x1 + ass, where a and as are constants. (e) Find the mean squared prediction error (MSPE) for the predictor that you found in (d). 2. Consider the function (h) defined by 1, (h): { h = 0, -0.5, h2, and otherwise. 0, (a) Show that y is an ACVF by providing a stationary process x that has y as its ACVF. (b) For the process with ACVF y, find the predictor 3. (c) What is the MSPE for x? 1. Consider the MA(2) process xwe + wt-1+ we-2, where we is a white noise process with mean O and variance 1. (a) Find the ACVF for xt. (b) Find the predictors x and x. (c) Suppose that we wish to predict 2 from 1 and 23. Find the best predictor of x2 of the form 2 = a1x1 + a3x3, where a and a3 are constants. (d) Suppose that we wish to predict 23 from 21 and 5. Find the best predictor of x3 of the form 3 = a1x1 + ass, where a and as are constants. (e) Find the mean squared prediction error (MSPE) for the predictor that you found in (d). 2. Consider the function (h) defined by 1, (h): { h = 0, -0.5, h2, and otherwise. 0, (a) Show that y is an ACVF by providing a stationary process x that has y as its ACVF. (b) For the process with ACVF y, find the predictor 3. (c) What is the MSPE for x?