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I see is rather more simple to implement than I sought!

A last favour, please, if possible!
There are some literature to help us to analyse historical and smoothed variables figures?
There must be something wrong with my delta_logoilprice_jp_obs (please find enclose figures from Historical and smoothed variables).

My model is a Log-linearization version. My relationships between Model variables and observed data are:

deltalog_gdp_jp_obs = c1logdeltagdp + (c1mugdpss - 1);// matched to non-demeaned growth rate, useful to estimation purposes
deltalog_gdp_for_obs = c2logdeltagdp + (c2mugdpss - 1);//matched to non-demeaned growth rate, useful to estimation purposes
dpcexfe_log_jp_obs = c1dcore ; //matched to log level, d1core is the net inflation
rer_log_jp_obs = c1rer ; //matched to log level, c1rer is the log exchange rate
dcomp_log_jp_obs = log(c1omega) ;
//c1omega is the model gross inflation and dcomp_log_jp_obs the observed net inflation

fedfunds_jp_obs = c1rs ;// matched to net interest rates, fedfunds_jp_obs is the net interest rate observation in quarterly form
fixi_share_jp_obs = ((exp(c1rpipd) * exp(c1i)) / exp(c1yd)) / c1rngdpy;
pce_share_jp_obs = ( ( (exp(c1rpcpd) * exp(c1c)) / exp(c1yd)) /c1rngdpy ) ;
exp_share_jp_obs = ( exp(c1x) / exp(c1yd) ) / c1rngdpy ;
imp_share_jp_obs = ( exp(c1m) / exp(c1yd) ) / c1rngdpy;

oilimp_share_jp_obs = exp(c1rpopd) * ( exp(c1o) / exp(c1y) - exp(c1yo) / exp(c1y) ) * (1 / c1rngdpy );
oilprod_jp_deltalog_obs = log(c1oy) - log(c1oy(-1)) + ( c1grmuoss - 1 );//matched to non-demeaned growth rate, useful to estimation purposes
oilprod_for_deltalog_obs = log(c2oy) - log(c2oy(-1)) + ( c2grmuoss - 1 );//matched to non-demeaned growth rate, useful to estimation purposes
delta_logoilprice_jp_obs = c1rpopd - c1rpopd(-1) + ( c1grmuzoss * c1mugdpss - c1grmuzss ) / c1grmuzss ; //matched to non-demeaned growth rate, useful to estimation purposes

Forget, I already found what was the problem!