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Econometrics is the application of statistical methods to economic data for various purposes such as of testing hypotheses, infering causal relationships and forecasting future trends. Only use this tag for questions relating to the theoretical aspect of an econometric technique.

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Estimate unobservable $X_t$ with observable estimation {$Y_t$}, where $Y_t= X_t+\delta e_t$

Suppose there are measurement values {$Y_t, Y_{t-1},..., Y_0$} which come from the relationship $Y_t= X_t+\delta e_t$, where $\delta$ is a known constant, $e_t\sim N(0,\sigma^2_e)$ is a Gaussian distr …
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