# Is the empirical mean the arithmetic mean?

**URL:** <https://forum.dynare.org/t/is-the-empirical-mean-the-arithmetic-mean/21851>\
**Category:** Stochastic simulations\
**Created:** [31 January 2023 06:04 UTC](https://forum.dynare.org/t/is-the-empirical-mean-the-arithmetic-mean/21851 "2023-01-31T06:04:41Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![mariale](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/e68b1a/32.png) [@mariale](https://forum.dynare.org/u/mariale)\
**Post date:** [31 January 2023 06:04 UTC](https://forum.dynare.org/t/is-the-empirical-mean-the-arithmetic-mean/21851/1 "2023-01-31T06:04:41Z")

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Hello,

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?

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [31 January 2023 10:48 UTC](https://forum.dynare.org/t/is-the-empirical-mean-the-arithmetic-mean/21851/2 "2023-01-31T10:48:06Z")

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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.

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**Author:** ![mariale](https://forum.dynare.org/letter_avatar_proxy/v4/letter/m/e68b1a/32.png) [@mariale](https://forum.dynare.org/u/mariale)\
**Post date:** [1 February 2023 06:05 UTC](https://forum.dynare.org/t/is-the-empirical-mean-the-arithmetic-mean/21851/3 "2023-02-01T06:05:11Z")

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Thank you, Prof. @jpfeifer