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I've been facing the problem of estimating a large PACF as the sample size grows.

My question is whether we can guarantee that the partial autocorrelation, estimated by the projection $X_t = \sum_{j=1}^n\phi_{n,j}X_{t-j}+\epsilon_t$, can converge uniformly (in probability) to it's populational values.

By now I have that the autocorrelation function does converge uniformly in probability. So, as we can interpret the PACF as a function of the ACF, can we state that it also converges uniformly?

Thanks

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