Consider the following autoregressive processes: Wn 2Wn-1 + Xn 3/4 Zn-1 + Xn Zo = 0....

 

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Consider the following autoregressive processes: Wn 2Wn-1 + Xn 3/4 Zn-1 + Xn Zo = 0. Zn = = Wo = 0 n (a) Suppose that X, is a Bernoulli process. What trends do the processes exhibit? Express W and Z, in terms of Xn, Xn-1,..., X₁ and then find E[W] and E[Z]. Do these results agree with the trends you expect? (b) n (c) Do W, or Z,, have independent increments? stationary increments? (d) Generate 100 outcomes of a Bernoulli process. Find the resulting realizations of W, and Zn. Is the sample mean meaningful for either of these processes? (e) Repeat part d if X, is the random step process. Consider the following autoregressive processes: Wn 2Wn-1 + Xn 3/4 Zn-1 + Xn Zo = 0. Zn = = Wo = 0 n (a) Suppose that X, is a Bernoulli process. What trends do the processes exhibit? Express W and Z, in terms of Xn, Xn-1,..., X₁ and then find E[W] and E[Z]. Do these results agree with the trends you expect? (b) n (c) Do W, or Z,, have independent increments? stationary increments? (d) Generate 100 outcomes of a Bernoulli process. Find the resulting realizations of W, and Zn. Is the sample mean meaningful for either of these processes? (e) Repeat part d if X, is the random step process.

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ANSWER a The processes exhibit linear trends b Wn Xn 2Xn1 n Zn 34Xn 34Xn1 EW EX 2EX 3EX n EZ 34... View the full answer