I am using this python package called CausalImpact (http://google.github.io/CausalImpact/) as one of the statistical methods in my research paper. I explained it in my methodology section as much as possible, but I am not confident on how to change the model equations to fit my variables. This is the paper that outlines the model that the package is using: https://projecteuclid.org/journals/annals-of-applied-statistics/volume-9/issue-1/Inferring-causal-impact-using-Bayesian-structural-time-series-models/10.1214/14-AOAS788.full
This is the state-space equations defined in the paper (they can be found on page 252):
y(t) =Z(t)*alpha(t) + error_term(t) and
alpha(t+1)=T(t)*alpha(t) + R(t)*n(t)
now, if my y(t) is inflation, and I have three covariates (25y yields, S&P500 closing price, exchange rate), how could I write these variables into the space-state equations provided?
As I currently understand, y(t) would be inflation, and alpha would be the vector of the three covariates, and the second equation would be the evolution of the three covariates over time?