Question: 11.2 Let {et : t 1,0,1, } be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a

11.2 Let {et : t 1,0,1, …} be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a stochastic process by xt et (1/2)et1 (1/2)et2, t 1,2,…. (i) Find E(xt ) and Var(xt ). Do either of these depend on t? (ii) Show that Corr(xt ,xt1) 1/2 and Corr(xt ,xt2) 1/3. (Hint: It is easiest to use the formula in Problem 11.1.) (iii) What is Corr(xt ,xth) for h 2? (iv) Is {xt } an asymptotically uncorrelated process?

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