# Seasonal Decomposition

The Seasonal Decomposition procedure decomposes a series into a seasonal component, a combined trend and cycle component, and an "error" component. The procedure is an implementation of the Census Method I, otherwise known as the ratio-to-moving-average method.

Example. A scientist is interested in analyzing monthly measurements of the ozone level at a particular weather station. The goal is to determine if there is any trend in the data. In order to uncover any real trend, the scientist first needs to account for the variation in readings due to seasonal effects. The Seasonal Decomposition procedure can be used to remove any systematic seasonal variations. The trend analysis is then performed on a seasonally adjusted series.

Statistics. The set of seasonal factors.

Seasonal Decomposition Data Considerations

Data. The variables should be numeric.

Assumptions. The variables should not contain any embedded missing data. At least one periodic date component must be defined. For instructions on handling missing data, see the topic on replacing missing values. To define a periodic date component, see the topic on defining dates.

Estimating Seasonal Factors

This feature requires the Forecasting option.

1. From the menus choose:

Analyze > Forecasting > Seasonal Decomposition...

2. Select one or more variables from the available list and move them into the Variable(s) list. Note that the list includes only numeric variables.

Model Type. The Seasonal Decomposition procedure offers two different approaches for modeling the seasonal factors: multiplicative or additive.

• Multiplicative. The seasonal component is a factor by which the seasonally adjusted series is multiplied to yield the original series. In effect, seasonal components that are proportional to the overall level of the series. Observations without seasonal variation have a seasonal component of 1.
• Additive. The seasonal adjustments are added to the seasonally adjusted series to obtain the observed values. This adjustment attempts to remove the seasonal effect from a series in order to look at other characteristics of interest that may be "masked" by the seasonal component. In effect, seasonal components that do not depend on the overall level of the series. Observations without seasonal variation have a seasonal component of 0.

Moving Average Weight. The Moving Average Weight options allow you to specify how to treat the series when computing moving averages. These options are available only if the periodicity of the series is even. If the periodicity is odd, all points are weighted equally.

• All points equal. Moving averages are calculated with a span equal to the periodicity and with all points weighted equally. This method is always used if the periodicity is odd.
• Endpoints weighted by .5. Moving averages for series with even periodicity are calculated with a span equal to the periodicity plus 1 and with the endpoints of the span weighted by 0.5.

Optionally, you can:

• Click Save to specify how new variables should be saved.

This procedure pastes SEASON command syntax.