Time Series Decomposition:
Y=TCSe. Fluctuation in trend & factors.
1. SI – Seasonal Index: Calculate SI, a.k.a S*e:
1.1. CMA (TC1): Centered Moving Average: TC1=Centered(2 shilfted years) all year moving Avg=avg of 2 MAs of 2 shifted years.
1.2. Single USI (Seasonal-Error): USI(t)=Y(t)/TC1.
1.3. USI=Average single USI’s of periods of same season.
1.4. ASI= USI*AF
2. Deseason: TC’=Yt*ASI
3. TC regression using TC’. Regression against t not Y(t-1).
Tt = a + bt
4. Forecasted Y=TC X SI
Decomposition in one picture: