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For a known mean zero, a common sample autocovariance function convention isThe weakly stationary process property gives $\mathbb{E}[Y_t{Y}_{t+h}]=\gamma (h)$, soThe lag-zero estimate is unbiased, but at nonzero lags the divisor $n$ causes a finite-sample multiplicative bias. An alternative convention uses $(n-h{)}^{-1}$ instead; for that convention the expectation is exactly $\gamma (h)$. These are two normalizations of the sample autocovariance function, so the divisor must be specified. Here no estimated-mean centering term occurs because zero is known. Replacing zero by a sample mean would introduce additional bias terms. Extend to negative lags by symmetry; there are no observed lagged pairs for $h\ge n$.

Replace the autocovariance in the finite-lag linear prediction equations by the sample autocovariance function. The last regression coefficient at order $k$ estimates the lag-$k$ partial autocorrelation function.