0
AR的Wold分解和自相关
是否可以使用Wold分解为AR(2)平稳模型检索到一定滞后的自相关(值或任何其他信息)? 例: Xt=0.32Xt−1+0.51Xt−2+εtXt=0.32Xt−1+0.51Xt−2+εtX_t=0.32X_{t-1}+0.51X_{t-2}+ \varepsilon_t 滞后聚形式 (1−0.32L−0.51L2)Xt=εt(1−0.32L−0.51L2)Xt=εt(1-0.32L-0.51L^2)X_t= \varepsilon_t 字符式 Z2−0.32Z−0.51=0Z2−0.32Z−0.51=0Z^2-0.32Z-0.51=0 尔德分解形式:(LJ:−ϕ1ψj−1−ϕ2ψj−2+ψj=0)(LJ:−ϕ1ψj−1−ϕ2ψj−2+ψj=0)(L^J:- \phi_1 \psi_{j-1}-\phi_2 \psi_{j-2}+ \psi_j = 0) L0:ψ0=0L0:ψ0=0L^0:\psi_0 = 0 L1:−0.32ψ0−ψ1=0L1:−0.32ψ0−ψ1=0L^1:-0.32 \psi_{0}-\psi_1 = 0 L2:−0.32ψ1−0.51ψ0+ψ2=0L2:−0.32ψ1−0.51ψ0+ψ2=0L^2:-0.32 \psi_{1}-0.51 \psi_{0}+ \psi_2 = 0 L3:−0.32ψ2−0.51ψ1+ψ3=0L3:−0.32ψ2−0.51ψ1+ψ3=0L^3:-0.32 \psi_{2}-0.51 \psi_{1}+ \psi_3 = 0 L4:−0.32ψ3−0.51ψ2+ψ4=0L4:−0.32ψ3−0.51ψ2+ψ4=0L^4:-0.32\psi_{3}-0.51 \psi_{2}+ \psi_4 = 0