In additional decomposition why should the seasonal indices add up to 0? And in multiplicative it should add up to m.? In additional the seasonal indices are positive and negative Yt= Tt + St + Rt If sum of St doesn't add up to 0, then St would have a net positive or negative effect in residual. In multiplicative decomposition Yt = Tt*St*Rt Rt = Yt/(Tt*St) Rt = (Yt/Tt)/m This would divide the residuals amongst the season periods according to indices. Is this explanation correct??
If we don't impose a constraint on St, there is an identifiability issue between St and Tt. It also ceases to be interpretable as a seasonal additive effect. Instead, it becomes some combination of seasonality and the level of the series, because there will be leakage from Tt to St without the constraint.
In additional decomposition why should the seasonal indices add up to 0?
And in multiplicative it should add up to m.?
In additional the seasonal indices are positive and negative
Yt= Tt + St + Rt
If sum of St doesn't add up to 0, then St would have a net positive or negative effect in residual.
In multiplicative decomposition
Yt = Tt*St*Rt
Rt = Yt/(Tt*St)
Rt = (Yt/Tt)/m
This would divide the residuals amongst the season periods according to indices.
Is this explanation correct??
If we don't impose a constraint on St, there is an identifiability issue between St and Tt. It also ceases to be interpretable as a seasonal additive effect. Instead, it becomes some combination of seasonality and the level of the series, because there will be leakage from Tt to St without the constraint.