When I detrend log of observed data with hp-filter algorithm, fluctuations of the series are typically around zero. But when I write a model in dynare in levels, take logs of the variables, and use hp_filter option, the simulated series does always fluctuate around zero. I know the mean does not matter much, kind of. But why the fluctuations of some model variables are sometimes not around zero, here C and I.

The simulated logged series still contain the mean. You need a proper observation equation. E.g.

```
y_obs=y-steadystate(y);
```

if `y=log(Y)`

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