Math

Published: 2021-06-29 06:44:34
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STAT 5160 HW41(1) (1-1.05B+0.4B2)Xt=Zt => Xt=1.05 Xt-1-0.4 Xt-2+ Zt, Zt~iid.N(0,1) => AR(2) model => stationarity condition:|φ2|1 + φ2 2 – φ1 |-0.4|  + (-0.4) = 0.65-0.4) – 1.05 =-1.45 This process is stationary(2) (1-1.05B)Xt=Zt => Xt=1.05 Xt-1+ Zt, Zt~iid.N(0,1) => AR(1) model => stationarity condition:|φ1||1.05|>1 which not satisfies the condition(3) (1+0.8B)Xt=(1-0.25B)Zt => Xt=-0.8Xt-1 + Zt – 0.25Zt-1, Zt~iid.N(0,1) => ARMA(1,1) model => stationarity condition: |φ1|1| stationarity condition: |-0.8| Both stationarity condition and invertibility contition satisfied => This process is stationary and invertible.

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