# How does Minitab do decomposition?

Decomposition involves the following steps:
1. Minitab smoothes the data using a centered moving average with a length equal to the length of the seasonal cycle. When the seasonal cycle length is an even number, a two-step moving average is required to synchronize the moving average correctly.
2. Minitab either divides the moving average into (multiplicative model) or subtracts it from (additive model) the data to obtain what are often referred to as raw seasonal values.
3. For corresponding periods of time in the seasonal cycles, Minitab determines the median of the raw seasonal values. For example, if you have 60 consecutive months of data (5 years), Minitab determines the median of the 5 raw seasonal values corresponding to January, to February, and so on.
4. Minitab adjusts the medians of the raw seasonal values so that their average is one (multiplicative model) or zero (additive model). These adjusted medians constitute the seasonal indices.
5. Minitab uses the seasonal indices to seasonally adjust the data.
6. Minitab fits a trend line to the seasonally adjusted data using least-squares regression.

The data can be detrended by either dividing the data by the trend component (multiplicative model) or subtracting the trend component from the data (additive model).

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