Difference between RMSE and SEE

[mmmask]

Hello,

What is the difference between Root mean squared error and standard error of estimate ?

Both are the root of the mean squared error ?

[125mph]

Apparently this topic has been debated quite a few times over the years… only a few people have it right

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91145028

@cpk123

in a sense - yes they are but the major difference - RMSE pertains to sample that is OUT OF PERIOD. It is based on Actual vs. Predicted for a future period sample outside of original regression. SEE - pertains to in period sample.

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9940883

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9731205

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9960158

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9701454

@naivejoe

RMSE is for out of sample to test how well the model is. MSE is a in-sample value, b/s it is not square root. it is mean of squared error.

[mmmask]

@TheAliMan

Ok several websites I have found say, RMSE = sqrt ( SSE / n) whereas SEE is sqrt ( SSE / (n-k-1)) I forgot the equation but there is an example in CFAI book

I believe this is the answer.

Can someone confirm pls

[tickersu]

@125mph

Apparently this topic has been debated quite a few times over the years… only a few people have it right

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91145028

@cpk123

in a sense - yes they are but the major difference - RMSE pertains to sample that is OUT OF PERIOD. It is based on Actual vs. Predicted for a future period sample outside of original regression. SEE - pertains to in period sample.

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9940883

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9731205

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9960158

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/9701454

@naivejoe

RMSE is for out of sample to test how well the model is. MSE is a in-sample value, b/s it is not square root. it is mean of squared error.

As far as I can tell working with people who have PhD Statistics backgrounds, and looking at actual statistics books, RMSE may be mentioned in forecasting, but they are the same for practical purposes. The mean square error (MSE) would be the error variance and RMSE would be the square root of that, which would be the error standard deviation. For what it’s worth, actual statisticians don’t usually use SEE or RMSE, in my experience, they refer to them by the universally understood terminology “model standard deviation”/ “standard deviation of the error term” or “model variance”/ “variance of the error term”, respectively, in the context of a regression. They will specify in-sample vs out of sample.