Time Series Decomposition

Time Series Decomposition:

Y=TCSe. Fluctuation in trend & factors.

Calculation Steps:
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:

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