I am developing a discrete health indicator model with $n$ multiple observations. The methodology is as follows: Every hour, my patients insert a subjective perception of various health indicators (tiredness, hunger, anxiety...) ranging from 0 to 10. This gives me a vector each hour, and I want to develop a matrix A such that:
$x_{t+1} = A*x_t + e_t$
where $A^{nxn}$ is supposed to tell me how the various indicators correlate or interact, and $e$ is white noise/error term. Given multiple observations $x$, how can I best approximate the matrix $A$? In college, we mostly used models like this with $A$ already known, and the state needed to be approximated...
