Residuals vs. Standardized Residuals

Econometrics questions and discussions

Residuals vs. Standardized Residuals

Unread postby ac_1 » Tue Apr 06, 2021 5:36 am

Hi Tom,

As per PRJ https://estima.com/ratshelp/index.html?prjinstruction.html, to calculate standardized residuals after a LINREG is

Code: Select all
prj(xvx=px)
set stdresids = resids/sqrt(%seesq*(1-px))
graph(style=symbols,vlabel="Standardized Residual")
# stdresids

I can get identical results via
Code: Select all
stats resids
set stdresids_2 = (resids - %mean) / sqrt(%variance)
prin / stdresids stdresids_2

However, sometimes after a BOXJENK, the former PRJ technique results in NA's, whereas the latter doesn't. Why?


Standardized residuals make it easier to view outliers:

(a) Should there be a comparison of both residuals and standardized residuals after a LINREG or BOXJENK via plots: line graph, histogram, acf & pacf, or just the standardized residuals?
(b) Are the standard diagnostic tests after a LINREG e.g. for heteroskedasticity (Breusch-Pagan-Godfrey, White's), autocorrelation (Durbin's H, Breusch-Godfrey), also valid after a BOXJENK, and if not, why not?


Cheers,
Amarjit
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Re: Residuals vs. Standardized Residuals

Unread postby TomDoan » Tue Apr 06, 2021 10:38 am

The calculation to which you are referring computes the standard error of projection allowing for the fact that the coefficients are estimated, rather than known. However, it doesn't apply to an ARMA model where the "data" themselves (the lagged residuals on the MA terms) are also subject to error. And in general it doesn't apply to non-linear models where the derivatives with respect to the parameters are evaluated at the estimated parameters.

Note that "standardized" residuals mean different things in different settings. In GARCH models, the residuals are typically standardized by dividing by the square root of the conditional variance---a calculation which is done taking the estimated parameters as fixed.
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Re: Residuals vs. Standardized Residuals

Unread postby ac_1 » Tue Apr 06, 2021 2:02 pm

Thanks. I can make various plots of the residuals after a BOXJENK e.g. @RegCorrs. How do I standardize the residuals?
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Re: Residuals vs. Standardized Residuals

Unread postby TomDoan » Wed Apr 07, 2021 9:21 am

I just explained that that is a calculation which doesn't apply to ARMA models. You can always do a simple standardization by dividing by the standard error of estimate (which is constant over the sample). "Big" residuals will be outside the +/- 2 range when scaled that way.
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Re: Residuals vs. Standardized Residuals

Unread postby ac_1 » Wed Apr 07, 2021 12:26 pm

Ok, but after demeaning:

Code: Select all
stats %resids
set stdresids = (%resids-%mean)/sqrt(%seesq)
stats stdresids
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Re: Residuals vs. Standardized Residuals

Unread postby TomDoan » Thu Apr 08, 2021 9:28 am

diff(standardize) will do that in a single step.
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