Time series decomposition
Time series decomposition
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Time series decomposition
Outline
1 Transformations and adjustments
2 Time series components
3 Moving averages
4 Classical decomposition
5 X-11 and SEATS decomposition
6 STL decomposition
2
Outline
1 Transformations and adjustments
2 Time series components
3 Moving averages
4 Classical decomposition
5 X-11 and SEATS decomposition
6 STL decomposition
3
Time series decomposition
Time series data can show a variety of patterns: trend, seasonality
and cycles.
It is useful to split a time series into several components where each
represents an underlying pattern category.
When decomposing a time series into components, we usually
combine the trend and cycle into a one trend-cycle component
(simply trend).
We can think that a time series is consist of three components:
trend-cycle, seasonal and remainder components.
We can expect to see more than one seasonal component, relating
to different seasonal periods (eg. with those observed at least daily).
Often time series decomposition is carried out to improve
understanding of the time series, but can also be used to improve
forecast accuracy.
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Transformations and adjustments
It is sometimes helpful to transform or adjust the data first before
decomposing.
We discuss four kinds of adjustments:
I Calendar adjustments
I Population adjustments
I Inflation adjustments
I Mathematical transformations
These adjustments and transformations simplify the patterns in data
by removing known sources of variation or making the pattern
consistent across the whole data set.
Simpler patterns are usually easier to model and lead to more
accurate forecasts.
5
Calendar adjustments
Some variation seen in seasonal data may be due to simple calendar
effects.
It is much easier to remove the variation before doing any further
analysis.
If we are studying monthly milk production on a farm, then there will
be variation between the months due to different number of days in
each month in addition to the seasonal variation across the year.
We can remove this variation by computing average milk production
per day in each month.
A similar adjustment can be done for the total monthly sales in a
retail store.