A GARCH model is a special case of a GAS volatility model when the measurement density is normal. When the measurement density is non-normal, the corresponding score that drives the model will be different. For example, using a t-distribution leads to 'trimming' of heavy-tailed observations, whereas using a GED distribution leads to 'Winsorization'. The normal score - aka the GARCH score- reacts linearly with respect to the residuals so does not have a similar robustness property.
If you have 4000 observations and you winsorize the top 2.5% and bottom 2.5% of data, then 200 observations will be affected. It doesn't matter what these values are, and it doesn't imply that they were outliers in any meaningful sense of the term.
Winsorizing data shouldn't remove any observations, but it will change them.
EDIT: Some additional information in response to comments.
One distinction to make is between trimming and Winsorization. Trimming will simply remove observations that fall outside of specified quantiles. So trimming to 95% will remove the top 2.5% of observations and the bottom 2.5% of observations.
Winsorizing doesn't remove observations, but changes the values of those observations outside a specified quantile to the value at that quantile. I think this makes sense with a simple example.
One word of caution is that there are different methods to find percentiles, so the defaults on other software packages may find somewhat different results.
Here, the data are Winsorized to 60%. The 20th percentile is calculated as 2.8 and the 80th percentile is calculated as 8.2. So the values less than 2.8 are replaced by 2.8 and the values greater than 8.2 are replaced with 8.2.
if(!require(psych)){install.packages("psych")}
A = c(1,2,3,4,5,6,7,8,9,10)
quantile (A, c(0.20, 0.80))
### 20% 80%
### 2.8 8.2
library(psych)
winsor(A, trim = 0.20) # This Winsorizes to the inner 60% of observations
### [1] 2.8 2.8 3.0 4.0 5.0 6.0 7.0 8.0 8.2 8.2
Best Answer
In a different, but related question on trimming that I just stumbled across, one answer had the following helpful insight into why one might use either winsorizing or trimming:
I'm curious if there is a more definitive approach, but the above logic sounds reasonable.