Question: Let {X4, t Z} be the ARMA(1, 2) process X = 0.2X,-1+ Z, + 4Z-2, {Z.}~WN(0, 3). (a) Is {X} causal? If yes, find

Let {X4, t Z} be the ARMA(1, 2) process X = 0.2X,-1+

Let {X4, t Z} be the ARMA(1, 2) process X = 0.2X,-1+ Z, + 4Z-2, {Z.}~WN(0, 3). (a) Is {X} causal? If yes, find the coefficients v, in the MA(oo) representation: X, = %3D (b) Is {X} invertible? If yes, find the coefficients n; in the AR(0) representation: Z = Eo T,Xi-j. (c) Determine the values of the PACF of {X:} at lags h = 0, 1, 2.

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