2. Chapter 5 The Decomposition Method

3. Components of a Time Series Trend - Tr t Seasonal - Sn t Cyclical - Cl t Irregular -  t

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

5. Two Models Additive Model: Multiplicative Model

6. Seasonal Deviations are the same each year! This is what we get with dummies

7. Seasonal Component grows with Y!

8. The MultiplicativeDecomposition (Ratio to Moving Average)

9. 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 don’t increase or decrease the average of your series

11. Start by estimating the trend and cyclical component using a centered moving average. For 1993:2, we calculate a centered moving average,.5*315.2 178.3 274.5 295.4.5*286.4 1049/4=262.25

13. Calculating the Seasonal Term Recall, that in our multiplicative model or rearranging terms,

14. 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

15. 274.5/262.5=1.046

16. 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!!!

17. 1.0467 0.9860 1.0515 1.0214 4.1056 4.1056 /4 =1.0264

18. A Neutral Adjustment The seasonal adjustment shouldn’t 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.

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