Dear Johannes,
In my DSGE model, all shocks follows an autoregressive processes except for price markup shock Vmt, which follows a autoregressive of order 1 and moving average of order 1 (ARMA(1,1)) process: Vm_t=Vm+\rho_m*(Vm_t(-1)-Vm)+epsilonm_t+\alpha*epsilonm_t(-1),
where Vm is steady state value of shock Vmt, Vmt(-1) is first order lag of Vmt, epsilonmt is price markup innovation, epsilonmt(-1) is first order lag of epsilonmt, rhom is autoregressive process.
epsilonmt follows a N(0,sigmam), where sigmam is standard deviation of innovation epsilonmt.
The number of observables equals the number of shocks,
My state space form is therefore:
Measurement equation Y_t=AS_t,
State transition equation S_t=BS_{t-1}+V_t
Shock process: V_t=\rho V_{t-1}+\epsilon^m_t+C\epsilon^m_{t-1}
where A is state to observable matrix, B is state transition matrix, \rho is a matrix who only has one nonzero element, and this nonzero element rho_m is located in one of the spaces in the diagonal, C is moving average parameter.
Therefore, do you think this state space form satisfy the condition of the existence of a DSGE-VAR model? Is the coexistence of ARMA(1,1) form of one structural shock and AR(1) of all other structural shock allowed for a DSGE-VAR model and can they identify al the structural shocks?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse
Having MA components in the shocks is generally not a problem. They will not affect the existence of a solution. Whether the shocks parameters are identified cannot be generally answered and needs to be checked for the particular model.