I’m using Andreasen et al (2018, REStud) higher order pruning method to simulate my model. I would like to set the initial value of state variables (vector x in their paper and code) equal to observed data values. The problem is that their stochastic simulation code requires initial values for first, second and third order effects. How should I connect the data values to the three sets of initial values?
simult_ takes the initial value as the first order term and sets all other terms to 0. That is the reason why all simulations use either a burnin period so that the starting point of simulations does not depend on the initial condition (essentially you start at the ergodic mean) or uses the stochastic steady state, which again is a unique combination of the three terms in the state space. However, if you only know the value of e.g. output at a point in time, you do not know which combination of first to third order term gave rise to this observation.