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In sources such as this one, someone would square the data before calculating ACF and PACF. However, it is not universally done. So should we square the time series data before calculating ACF and PACF? Or should it be done depending on cases?
If the purpose of squaring the data is to get rid of the effect of different sign: then why don't we just take the absolute value?
ACF and PACF of (raw/levels) returns tells us something about the conditional mean of returns. If there are some significant values, an ARMA model may be relevant.
ACF and PACF of squared returns tells us something about the conditional variance of returns*. If there are some significant values, a GARCH model may be relevant. Regarding squaring vs. taking the absolute values, a stylized fact about financial returns says that the dependence is typically stronger in squares than in absolute values. Therefore, if we want to find and model autoregressive patterns, we may succeed better by looking at squares.
*Especially if there are no significant ACF/PACF values of raw/levels returns. Otherwise it makes sense to check the ACF and PACF of squared residuals from the conditional mean model.
