1. Given X = 0.7 X-1 +Z+0.2 Zt-1- a. Is it stationary? b. Express the ARMA(1,1)...

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1. Given X = 0.7 X-1 +Z+0.2 Zt-1- a. Is it stationary? b. Express the ARMA(1,1) process as an infinity moving average process. c. Express the ARMA(1,1) process as an infinity autoregressive process. d. Find the autocorrelation of it at lag 1. e. Find the autocorrelation of it at lag 2. f. Find the autocorrelation of it at lag 3. 3.1 Determine which of the following ARMA processes are causal and which of them are invertible. (In each case {Z,) denotes white noise.) (a) X, +0.2X,1 -0.48X-2= Z₁. (b) X, +1.9X,-1+0.88X-2=Z₁ +0.2Z₁-1 +0.7Z1-2. (c) X₁ +0.6X₁-1 = Z₁ + 1.2Z-1. (d) X, +1.8X,-1+0.81X1-2 = Z₁. (e) X₁ + 1.6X-1 = Z₁ -0.4Z-1 +0.04Z1-2. 3.3 For those processes in Problem 3.1 that are causal, compute the first six co- efficients Vo, V1,...,s in the causal representation X, jo ViZ₁-; of {X₁}. 3.4 Compute the ACF and PACF of the AR(2) process X₁ = 0.8X₁-2 +Z₁, (Z)~WN (0,0²). 1. Given X = 0.7 X-1 +Z+0.2 Zt-1- a. Is it stationary? b. Express the ARMA(1,1) process as an infinity moving average process. c. Express the ARMA(1,1) process as an infinity autoregressive process. d. Find the autocorrelation of it at lag 1. e. Find the autocorrelation of it at lag 2. f. Find the autocorrelation of it at lag 3. 3.1 Determine which of the following ARMA processes are causal and which of them are invertible. (In each case {Z,) denotes white noise.) (a) X, +0.2X,1 -0.48X-2= Z₁. (b) X, +1.9X,-1+0.88X-2=Z₁ +0.2Z₁-1 +0.7Z1-2. (c) X₁ +0.6X₁-1 = Z₁ + 1.2Z-1. (d) X, +1.8X,-1+0.81X1-2 = Z₁. (e) X₁ + 1.6X-1 = Z₁ -0.4Z-1 +0.04Z1-2. 3.3 For those processes in Problem 3.1 that are causal, compute the first six co- efficients Vo, V1,...,s in the causal representation X, jo ViZ₁-; of {X₁}. 3.4 Compute the ACF and PACF of the AR(2) process X₁ = 0.8X₁-2 +Z₁, (Z)~WN (0,0²).

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a No it is not stationary as the coefficient of Xt1 is nonzero and greater than 1 in absolute value ... View the full answer