I am not quite sure if I correctly understand Remark 14 of your book ,so post this and hope you could have a look.

The production function in my model only has transitory technology shock, so there is no trend. In terms of the data, I take first difference of y, c , I ,h.

The data shows the average growth rate of y c I h is 0.0040, 0.0045, 0.0030, 0.000 respectively.

Model is loglinearized.

Then I should specify measurement equation like
y_obs=y-y(-1)+0.004;
c_obs=c-c(-1)+0.004;
i_obs=i-i(-1)+0.004;
h_obs=h-h(-1);

Should I use **only mean output growth rate **to demean growth rates data of y, c, I

OR

use the **mean output growth rate **to demean growth rates data of y, while use the mean consumption growth rate to demean growth rates data of c…so on so forth ?

Of course it depends. That’s what the remark about cointegrating relationships is about. But for most practical purposes, demean all series separately.