Question: Let 5et : t 5 21, 0, 1, p6 be a sequence of independent, identically distributed random variables with mean zero and variance one. Define

Let 5et

: t 5 21, 0, 1, p6 be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a stochastic process by xt 5 et 2 11/22et21 1 11/22et22, t 5 1, 2, p.

(i) Find E1xt 2 and Var1xt 2. Do either of these depend on t?

(ii) Show that Corr1xt

, xt11 2 5 21/2 and Corr1xt

, xt12 2 5 1/3. (Hint: It is easiest to use the formula in Problem 1.)

(iii) What is Corr1xt , xt1h 2 for h . 2?
(iv) Is 5xt 6 an asymptotically uncorrelated process?

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