I am a bit confused as to why the SARIMA model requires four parameters beyond the ARMIA model just to remove the seasonal component from a time series.
Obviously $m$ is required to specify the duration of the period. It is less clear how $P$, $D$, and $Q$ jointly specify the remainder of the information about seasonality.
Does removing seasonality ultimately consist of removing or quieting certain terms from a frequency domain representation of a time series, in the same mathematical vein as removing a target frequency from audio? If so, then how would the four parameters $m$, $P$, $D$, and $Q$ relate to targeting a frequency in the audio engineering application?