GARCH is Generalized AutoRegressive Conditional Heteroskedasticity.
It is written in online notes that series need to be stationary before using it for GARCH modeling, and usually the RETURNS series are stationary.
But online notes also say that the series needs to have heteroscedasticity (variable conditional variance) in order to apply GARCH on it, so how can a series be stationary as well as heteroscedastic.
Похоже на терминологическую путаницу. У стационарных рядов дисперсия не меняется.
Note that ARCH and GARCH model conditional heteroskedasticity. Although it would not be super precise, we can say that stationarity holds considering unconditional expectations, so that stationary time series - like stock returns - have constant (unconditional) moments which vary over (i.e., conditionally to) time. In other words, variance is function of time, although the time series has a constant unconditional mean. Note also that, for example, the ARCH model has a constant and finite unconditional variance under some regularity conditions, so that it is a stationary process too.
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