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I am trying to gain an understanding of the CausalImpact package and the BSTS approach. Consider the following model:

$y_t = \mu_t + z_t + \epsilon_t$, where $\epsilon_t \sim N(0,s^2)$, and $\mu_{t+1} = \mu_t + \eta_t$, where $\eta_t \sim N(0,s'^2)$, and $z_t = \beta x_t$ where $x_t$ is the control time series.

Am I correct in thinking that the default mode in the CausalImpact package employs the above model?

Now, with the default options, if I explicitly incorporate the time $t$ itself as a control time-series (as a covariate within $x$), will I recover the local linear trend model?

Thanks.

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