Is the empirical mean the arithmetic mean?


I have a small question on empirical mean. To check the model fitness I need to compare the empirical mean to the theoretical one. In my data, I have GDPpc (Y), Consumption (C). As Professor Pfeifer suggests, to get Yobs and Cobs I took {\log{Y_t^{data}}} and {\log{C_t^{data}}} applied one-sided HP-filter (except for interest rate) to it in Eviews. Is my empirical mean of my data, Y, would be the arithmetic mean of filtered {\log{Y_t^{data}}}? Or other types of mean?

The one-sided HP filter will demean the series. Thus, you should asymptotically get a mean of 0. In any case, you should compare filtered objects in the data to the ones in the model.

Thank you, Prof. @jpfeifer