# Default CausalImpact Package

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.