2. Given a probability space (12, F,P). A time series process X.t e Z is called a weakly stationary process, if (1) E(X)

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2 Given A Probability Space 12 F P A Time Series Process X T E Z Is Called A Weakly Stationary Process If 1 E X 1 (34.49 KiB) Viewed 73 times

2. Given a probability space (12, F,P). A time series process X.t e Z is called a weakly stationary process, if (1) E(X) = constant, Vt e Z; and (2) Cov(X4, Xx) = plt - s), Vt, s € Z, for some function p: Z R. Let the times series process X = {X/(w): € NW EN} be defined as X/(w) := sin(t +U(w)), te NW EN where U : N2 + (-27,0) be a uniformly distributed random variable on (2, F,P). Prove that X is a weakly stationary process. [20 Marks] {Hint: use the identity: sin(A) sin(B) = } [cos(A - B) - cos(A + B)].}