Convergence Diagnostics in Smets Wouters model

I was checking the Geweke convergence diagnostics by slightly modifying the mod file of Johannes Pfeifer. I find a number of parameters for which equality of means is decisively rejected at 450,000 iterations (included loaded iterations). The trace plots indicate particularly severe variations in the moving average for crhob, csadjcost, chabb, crdy, and ctrend.

My question is to what extent these convergence issues are a concern and what follow-up checks can be done. This is an important case study to form good practices on convergence issues for other work.

Thank you very much

TracePlot_crhob_blck_1.eps (268.8 KB) TracePlot_chabb_blck_1.eps (265.6 KB) TracePlot_crdy_blck_1.eps (268.4 KB) TracePlot_ctrend_blck_1.eps (267.0 KB) TracePlot_csadjcost_blck_1.eps (270.5 KB) Smets_Wouters.mod (22.1 KB)
usmodel_shock_decomp_mode.mat (8.5 KB)

There is clear evidence here of bi-modality, i.e. the posterior distribution has two modes and the chain oscillates between the two. How does the trace plot of the posterior density look like?