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Is there any other method to compute the sample autocorrelation function (ACF) of AR(p), the p$^{th}$ autoregressive model except the Yule-Walker equations?

I want to determine if ACF is 0 except at lags 1,5,6,7 for the model:

$X_t$ =$Z_t$+ $\phi_1$$X_{t-1}$+ $\phi_5$$X_{t-5}$ + $\phi_6$$X_{t-6}$ + $\phi_7$$X_{t-7}$

And if the ACF is 0 except at lags 1,5,6,7 for this:

$X_t$ =$Z_t$+ $\phi_1$$X_{t-1}$+ $\phi_5$$X_{t-5}$ + $\phi_6$$X_{t-6}$

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