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Problem 2 (10 pts). Identify the following models as ARMA(p,q) models (watch out for parameter redundancy), and determine whether they are causal and/or invertible. In each case {W_t} ~ wn(0,1). If any model is shown to be causal, then further compute its corresponding first five coefficients ?0, ?1, ?2, ?3, ?4 in the causal linear process representation X_t = sum_{j=0}^infty ?_j W_{t-j}. a) X_t = 0.8 X_{t-1} - 0.15 X_{t-2} + W_t - 0.3 W_{t-1} b) X_t = X_{t-1} - 0.5 X_{t-2} + W_t - W_{t-1} c) X_t - (9/4) X_{t-1} - (9/4) X_{t-2} = W_t - 3 W_{t-1} + (1/9) W_{t-2} - W_{t-3}

          Problem 2 (10 pts). Identify the following models as ARMA(p,q) models (watch out for parameter redundancy), and determine whether they are causal and/or invertible. In each case {W_t} ~ wn(0,1). If any model is shown to be causal, then further compute its corresponding first five coefficients ?0, ?1, ?2, ?3, ?4 in the causal linear process representation X_t = sum_{j=0}^infty ?_j W_{t-j}.

a) X_t = 0.8 X_{t-1} - 0.15 X_{t-2} + W_t - 0.3 W_{t-1}

b) X_t = X_{t-1} - 0.5 X_{t-2} + W_t - W_{t-1}

c) X_t - (9/4) X_{t-1} - (9/4) X_{t-2} = W_t - 3 W_{t-1} + (1/9) W_{t-2} - W_{t-3}

Problem 2 (10 pts). Identify the following models as ARMA(p,q) models (watch out for parameter redundancy), and determine whether they are causal and/or invertible. In each case Wt wn(0,1). If any model is shown to be causal, then further compute its corresponding first five coefficients ?0, ?1, ?2, ?3, ?4 in the causal linear process representation Xt = sumj=0^infty ?j Wt-j.

a) Xt = 0.8 Xt-1 - 0.15 Xt-2 + Wt - 0.3 Wt-1

b) Xt = Xt-1 - 0.5 Xt-2 + Wt - Wt-1

c) Xt - (9/4) Xt-1 - (9/4) Xt-2 = Wt - 3 Wt-1 + (1/9) Wt-2 - Wt-3

Added by Shannon P.

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