The Decomposition Method

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Chapter 5

• The Decomposition Method

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Components of a Time Series

• Trend - Trt
• Seasonal - Snt
• Cyclical - Clt
• Irregular - et

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Our Goal is to find break the varable into these
parts.
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Two Models

• Additive Model
• Multiplicative Model

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Seasonal Deviations are the same each year! This
is what we get with dummies
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Seasonal Component grows with Y!
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The MultiplicativeDecomposition(Ratio to Moving
Average)
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Steps

• 1. Calculate a centered moving average
• 2. Take the ratio of your variable to its moving
  average
• 3. Use the average of all ratios in the same
  quarter as the tentative seasonal index
• 4. Adjust to make sure you dont increase or
  decrease the average of your series

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Start by estimating the trend and cyclical
component using a centered moving average.
For 19932, we calculate a centered moving
average, .5315.2 178.3 274.5 295.4 .5286.4 1049
/4262.25
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Calculating the Seasonal Term

• Recall, that in our multiplicative model
• or rearranging terms,

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Calculations (cont.)

• The centered moving average is an estimate of the
  trend and cyclical component (TrCl)
• Thus an estimate of the seasonal component (times
  some error) is the ratio to moving average

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274.5/262.51.046
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Finishing it up!

• Note that the seasonal component for each quarter
  should be the same in every year
• The seasonal component in the first quarter of
  1994 should be the same as the seasonal component
  in the first quarter of 1996
• Just use the average over all first quarters as
  the seasonal component!!!

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1.0467 0.9860 1.0515 1.0214 4.1056 4.1056
/4 1.0264
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A Neutral Adjustment

• The seasonal adjustment shouldnt raise or lower
  the average value of the series.
• Multiplying the current seasonal adjustment by
  4/(sum of current adjustments) takes cares of
  this problem.

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Point and click gives you a choice of seasonal
adjustments in E-views!