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2.2: Estimation of the Autocovariance Function
https://stats.libretexts.org/Bookshelves/Advanced_Statistics/Time_Series_Analysis_(Aue)/2%3A_The_Estimation_of_Mean_and_Covariances/2.2%3A_Estimation_of_the_Autocovariance_Function
The estimator $\hat{\rho}(h)$ is consistent for $\rho(h)$ under an appropriate set of assumptions, that is, $\mathrm{Var}(\hat{\rho}(h)-\rho(h))\to 0$ as $n\to\infty$ . For $m\geq 1$ , let \(\...The estimator $\hat{\rho}(h)$ is consistent for $\rho(h)$ under an appropriate set of assumptions, that is, $\mathrm{Var}(\hat{\rho}(h)-\rho(h))\to 0$ as $n\to\infty$ . For $m\geq 1$ , let $\mathbf{\rho}_m=(\rho(1),\ldots,\rho(m))^T$ and $\mathbf{\hat{\rho}}_m=(\hat{\rho}(1),\ldots,\hat{\rho}(m))^T$ , where $^T$ denotes the transpose of a vector.

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