Dear Prof.
During Bayesian estimation, I can get the postior modes, but still with the following problems:
POSTERIOR KERNEL OPTIMIZATION PROBLEM!
(minus) the hessian matrix at the “mode” is not positive definite!
=> posterior variance of the estimated parameters are not positive.
You should try to change the initial values of the parameters using
the estimated_params_init block, or use another optimization routine.
and
Log data density [Laplace approximation] is NaN.
Dynare could proceed to report IRFs and other results. But except mode, it doesn’t give me postior standard deviations of parameters. For example:
RESULTS FROM POSTERIOR ESTIMATION
parameters
prior mean mode s.d. prior pstdev
omega 2.000 0.9196 NaN gamm 2.0000
I tried the following method to find the problem, but failed.

model_diagnostics
detected no problems. 
mode_check
seems fine. There are only two big red dots for one parameter. 
prior simulate
detected no problems
Prior mass = 1
BK indeterminacy share = 0
BK unstability share = 0
BK singularity share = 0
Complex jacobian share = 0
mjdgges crash share = 0
Steady state problem share = 0
Complex steady state share = 0
Analytical steady state problem share = 0
 Besides, I’m concerned about the problem of data. I used differences of logs of data to match variables in model. I also introduced trends of fill the gaps between the steady states of model and data.
Here are mode_check plots
It there any other method to fix my problem?
I attach my mod file and data in the following. Thanks!
FY