2: The Estimation of Mean and Covariances
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In this brief second chapter, some results concerning asymptotic properties of the sample mean and the sample ACVF are collected. Throughout, (Xt:t∈Z) denotes a weakly stationary stochastic process with mean μ and ACVF γ. In Section 1.2 it was shown that such a process is completely characterized by these two quantities. The mean μ was estimated by the sample mean ˉx, and the ACVF γ by the sample ACVF ˆγ defined in (1.2.1). In the following, some properties of these estimators are discussed in more detail.