# Wold Decomposition and autocorrelations of AR

Is it possible to retrieve Autocorrelations ( value or any other info) up to a certain lag for an AR(2) stationary model using the Wold decomposition?

Example:

$$X_t=0.32X_{t-1}+0.51X_{t-2}+ \varepsilon_t$$

Lag Poly Form

$$(1-0.32L-0.51L^2)X_t= \varepsilon_t$$

Char Eq

$$Z^2-0.32Z-0.51=0$$

Wold Decomposition form $(L^J:- \phi_1 \psi_{j-1}-\phi_2 \psi_{j-2}+ \psi_j = 0)$:

$L^0:\psi_0 = 0$

$L^1:-0.32 \psi_{0}-\psi_1 = 0$

$L^2:-0.32 \psi_{1}-0.51 \psi_{0}+ \psi_2 = 0$

$L^3:-0.32 \psi_{2}-0.51 \psi_{1}+ \psi_3 = 0$

$L^4:-0.32\psi_{3}-0.51 \psi_{2}+ \psi_4 = 0$

• enter link description here the ACVF is a function that tails of and the ACF is the ACVF divided by the variance of the function – user4314 Mar 31 '15 at 19:07