Initial value doesn't fade away

Hi professor, I estimated on a two country model and plot the hist decomposition. However, for some variables, the initial values fade away, but for some other variables, the initial value keeps constant. for all observed variables, I did sequently: seasonally adjusted, log and one-sided filter. Could you please give me any hint about what happens and how to solve this problem? Thank you so much for your help.

You can verify that some of your observables are not mean 0. For the model to explain the non-zero mean, it requires near unit root behavior, which also mean that effect of shocks and therefore the initial condition as well is (almost) permanent.

Thank you professor for your suggestion. I have three questions.

  1. With your suggestion, I demean some observed variables so that all their mean are zero. However, the initial values still perform permanent. The Does that mean that something is wrong with my model and estimation? How should I solve this problem? Thank you professor for your help.

  2. The initial value of output growth which is also the observed variable fades away quickly, but the initial value of output doesn’t fade away as the above picture shows. What does this situation imply? How can I solve this problem ?

  3. Actually, I already apply one-sided HP filter to all observed data although some of them still don’t have mean zero. My question is that can I just let the permanent initial value be? I thought from the perspective of equivalence, after three treatment of seasonally adjusted, log and filter, the observed data could sufficiently be matching up with the variables in the model. I could not clearly get the underlying reason that I need demean the data. I know my understanding might makes some mistakes. Could you please correct me? Thank you so much for your help.