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Time Series Problem

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Let {Z(s), s } is a stationary process. Define
Suppose (Z(s1),....,Z(sn)) is observed at know locations {s1,....,sn}. Please find an optimal linear prediction of Z(s) based on the observations and function. How would you estimate function from the observations?
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There is an attached solution of the estimation function from the observations. The solution is a step by step time series solution.

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