estimation targeting a fixed number of steps ahead

[elray1]

in the model section of the stan file, rather than calculating the likelihood, calculate the log predictive density h steps after the last time point. Probably want to write a helper function to do this calculation.

Function: lssm_constant_forecast_log_score (or similar)

Inputs:

• LSSM matrices
• observed data y
• horizon h

Logic:

• initialize return value = 0
• for t in 1:(n - h):
  • update filtering up through time t
  • obtain mean and covariance of forecast distribution at time t + h
  • return value += log predictive density at time t + h evaluated at y[t + h]

Then in the model section of stan file, call target += lssm_constant_forecast_log_score(...)