According to what I have found so far, in order to implement ARIMA we need to have a stationary (constant mean and variance) transformed data set. In addition, I have also seen that the square of the residuals may be in relation as a result of an ARIMA model, which is why we involve an ARCH or GARCH model. Actually, volatility (variance) may be time-dependent as a result of ARIMA.
How is it possible that although our transformed data have constant variance, in order to implement the ARIMA model, the sum of squared residuals, which means variance as a result of the ARIMA model, may not be constant (time-dependent)?
We say that to employ ARIMA we need to have constant variance data, but afterwards according to the residuals of ARIMA we can see that variance is not constant and time-dependent, so let's include an ARCH GARCH model? Isn't this a contradiction?