Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Deseasonalizing Forecasts by ahmad bassiouny 23348 views
- Business Forecasting (Decomposition... by Duke Shu 2017 views
- ForecastIT 7. Decomposition by DeepThought, Inc. 990 views
- Forecasting Techniques - Data Scien... by Kai Xin Thia 1192 views
- CCW Conference Environment Justice by Clean Water 200 views
- Criminal Justice System Today by Luis Lebron 152 views

10,367 views

10,061 views

10,061 views

Published on

No Downloads

Total views

10,367

On SlideShare

0

From Embeds

0

Number of Embeds

3

Shares

0

Downloads

221

Comments

0

Likes

2

No embeds

No notes for slide

- 1. Classical Decomposition Boise State University By: Kurt Folke Spring 2003
- 2. Overview: <ul><li>Time series models & classical decomposition </li></ul><ul><li>Brainstorming exercise </li></ul><ul><li>Classical decomposition explained </li></ul><ul><li>Classical decomposition illustration </li></ul><ul><li>Exercise </li></ul><ul><li>Summary </li></ul><ul><li>Bibliography & readings list </li></ul><ul><li>Appendix A: exercise templates </li></ul>
- 3. Time Series Models & Classical Decomposition <ul><li>Time series models are sequences of data that follow non-random orders </li></ul><ul><li>Examples of time series data: </li></ul><ul><ul><li>Sales </li></ul></ul><ul><ul><li>Costs </li></ul></ul><ul><li>Time series models are composed of trend, seasonal, cyclical, and random influences </li></ul>
- 4. Time Series Models & Classical Decomposition <ul><li>Decomposition time series models: </li></ul><ul><li>Multiplicative: Y = T x C x S x e </li></ul><ul><li>Additive: Y = T + C + S + e </li></ul><ul><li>T = Trend component </li></ul><ul><li>C = Cyclical component </li></ul><ul><li>S = Seasonal component </li></ul><ul><li>e = Error or random component </li></ul>
- 5. Time Series Models & Classical Decomposition <ul><li>Classical decomposition is used to isolate trend, seasonal, and other variability components from a time series model </li></ul><ul><li>Benefits: </li></ul><ul><ul><li>Shows fluctuations in trend </li></ul></ul><ul><ul><li>Provides insight to underlying factors affecting the time series </li></ul></ul>
- 6. Brainstorming Exercise <ul><li>Identify how this tool can be used in your organization… </li></ul>
- 7. Classical Decomposition Explained <ul><li>Basic Steps: </li></ul><ul><li>Determine seasonal indexes using the ratio to moving average method </li></ul><ul><li>Deseasonalize the data </li></ul><ul><li>Develop the trend-cyclical regression equation using deseasonalized data </li></ul><ul><li>Multiply the forecasted trend values by their seasonal indexes to create a more accurate forecast </li></ul>
- 8. Classical Decomposition Explained: Step 1 <ul><li>Determine seasonal indexes </li></ul><ul><li>Start with multiplicative model… </li></ul><ul><li>Y = TCSe </li></ul><ul><li>Equate… </li></ul><ul><li>Se = (Y/TC) </li></ul>
- 9. Classical Decomposition Explained: Step 1 <ul><li>To find seasonal indexes, first estimate trend-cyclical components </li></ul><ul><li>Se = (Y/ TC ) </li></ul><ul><li>Use centered moving average </li></ul><ul><ul><li>Called ratio to moving average method </li></ul></ul><ul><li>For quarterly data, use four-quarter moving average </li></ul><ul><ul><li>Averages seasonal influences </li></ul></ul>Example
- 10. Classical Decomposition Explained: Step 1 <ul><li>Four-quarter moving average will position average at… </li></ul><ul><ul><ul><li>end of second period and </li></ul></ul></ul><ul><ul><ul><li>beginning of third period </li></ul></ul></ul><ul><li>Use centered moving average to position data in middle of the period </li></ul>Example
- 11. Classical Decomposition Explained: Step 1 <ul><li>Find seasonal-error components by dividing original data by trend-cyclical components </li></ul><ul><li>Se = ( Y/TC ) </li></ul><ul><li>Se = Seasonal-error components </li></ul><ul><li>Y = Original data value </li></ul><ul><li>TC = Trend-cyclical components </li></ul><ul><li>(centered moving average value) </li></ul>Example
- 12. Classical Decomposition Explained: Step 1 <ul><li>Unadjusted seasonal indexes (USI) are found by averaging seasonal-error components by period </li></ul><ul><li>Develop adjusting factor (AF) so USIs are adjusted so their sum equals the number of quarters (4) </li></ul><ul><ul><li>Reduces error </li></ul></ul>Example Example
- 13. Classical Decomposition Explained: Step 1 <ul><li>Adjusted seasonal indexes (ASI) are derived by multiplying the unadjusted seasonal index by the adjusting factor </li></ul><ul><li>ASI = USI x AF </li></ul><ul><li>ASI = Adjusted seasonal index </li></ul><ul><li>USI = Unadjusted seasonal index </li></ul><ul><li>AF = Adjusting factor </li></ul>Example
- 14. Classical Decomposition Explained: Step 2 <ul><li>Deseasonalized data is produced by dividing the original data values by their seasonal indexes </li></ul><ul><li>( Y/S ) = TCe </li></ul><ul><li>Y/S = Deseasonalized data </li></ul><ul><li>TCe = Trend-cyclical-error component </li></ul>Example
- 15. Classical Decomposition Explained: Step 3 <ul><li>Develop the trend-cyclical regression equation using deseasonalized data </li></ul><ul><li> T t = a + bt </li></ul><ul><li>T t = Trend value at period t </li></ul><ul><li>a = Intercept value </li></ul><ul><li>b = Slope of trend line </li></ul>Example
- 16. Classical Decomposition Explained: Step 4 <ul><li>Use trend-cyclical regression equation to develop trend data </li></ul><ul><li>Create forecasted data by multiplying the trend data values by their seasonal indexes </li></ul><ul><ul><li>More accurate forecast </li></ul></ul>Example Example
- 17. Classical Decomposition Explained: Step Summary <ul><li>Summarized Steps: </li></ul><ul><li>Determine seasonal indexes </li></ul><ul><li>Deseasonalize the data </li></ul><ul><li>Develop the trend-cyclical regression equation </li></ul><ul><li>Create forecast using trend data and seasonal indexes </li></ul>
- 18. Classical Decomposition: Illustration <ul><li>Gem Company’s operations department has been asked to deseasonalize and forecast sales for the next four quarters of the coming year </li></ul><ul><li>The Company has compiled its past sales data in Table 1 </li></ul><ul><li>An illustration using classical decomposition will follow </li></ul>
- 19. Classical Decomposition Illustration: Step 1 <ul><li>(a) Compute the four-quarter simple moving average </li></ul><ul><li>Ex: simple MA at end of Qtr 2 and beginning of Qtr 3 </li></ul><ul><li>(55+47+65+70)/4 = 59.25 </li></ul>Explain
- 20. Classical Decomposition Illustration: Step 1 <ul><li>(b) Compute the two-quarter centered moving average </li></ul><ul><li>Ex: centered MA at middle of Qtr 3 </li></ul><ul><li>(59.25+61.25)/2 </li></ul><ul><li>= 60.500 </li></ul>Explain
- 21. Classical Decomposition Illustration: Step 1 <ul><li>(c) Compute the seasonal-error component (percent MA) </li></ul><ul><li>Ex: percent MA at Qtr 3 </li></ul><ul><li>(65/60.500) </li></ul><ul><li>= 1.074 </li></ul>Explain
- 22. Classical Decomposition Illustration: Step 1 <ul><li>(d) Compute the unadjusted seasonal index using the seasonal-error components from Table 2 </li></ul><ul><li>Ex (Qtr 1): [(Yr 2, Qtr 1) + (Yr 3, Qtr 1) + (Yr 4, Qtr 1)]/3 </li></ul><ul><li>= [0.989+0.914+0.926]/3 = 0.943 </li></ul>Explain
- 23. Classical Decomposition Illustration: Step 1 <ul><li>(e) Compute the adjusting factor by dividing the number of quarters (4) by the sum of all calculated unadjusted seasonal indexes </li></ul><ul><li>= 4.000/(0.943+0.851+1.080+1.130) = (4.000/4.004) </li></ul>Explain
- 24. Classical Decomposition Illustration: Step 1 <ul><li>(f) Compute the adjusted seasonal index by multiplying the unadjusted seasonal index by the adjusting factor </li></ul><ul><li>Ex (Qtr 1): 0.943 x (4.000/4.004) = 0.942 </li></ul>Explain
- 25. Classical Decomposition Illustration: Step 2 <ul><li>Compute the deseasonalized sales by dividing original sales by the adjusted seasonal index </li></ul><ul><li>Ex (Yr 1, Qtr 1): </li></ul><ul><li>(55 / 0.942) </li></ul><ul><li>= 58.386 </li></ul>Explain
- 26. Classical Decomposition Illustration: Step 3 <ul><li>Compute the trend-cyclical regression equation using simple linear regression </li></ul><ul><li>T t = a + bt </li></ul><ul><li>t-bar = 8.5 </li></ul><ul><li>T-bar = 69.6 </li></ul><ul><li>b = 1.465 </li></ul><ul><li>a = 57.180 </li></ul><ul><li>T t = 57.180 + 1.465t </li></ul>Explain
- 27. Classical Decomposition Illustration: Step 4 <ul><li>(a) Develop trend sales </li></ul><ul><li>T t = 57.180 + 1.465t </li></ul><ul><li>Ex (Yr 1, Qtr 1): </li></ul><ul><li>T 1 = 57.180 + 1.465(1) = 58.645 </li></ul>Explain
- 28. Classical Decomposition Illustration: Step 4 <ul><li>(b) Forecast sales for each of the four quarters of the coming year </li></ul><ul><li>Ex (Yr 5, Qtr 1): </li></ul><ul><li>0.942 x 82.085 </li></ul><ul><li>= 77.324 </li></ul>Explain
- 29. Classical Decomposition Illustration: Graphical Look
- 30. Classical Decomposition: Exercise <ul><li>Assume you have been asked by your boss to deseasonalize and forecast for the next four quarters of the coming year (Yr 5) this data pertaining to your company’s sales </li></ul><ul><li>Use the steps and examples shown in the explanation and illustration as a reference </li></ul><ul><li>Basic Steps </li></ul><ul><li>Explanation </li></ul><ul><li>Illustration </li></ul><ul><li>Templates </li></ul>
- 31. Summary <ul><li>Time series models are sequences of data that follow non-arbitrary orders </li></ul><ul><li>Classical decomposition isolates the components of a time series model </li></ul><ul><li>Benefits: </li></ul><ul><ul><li>Insight to fluctuations in trend </li></ul></ul><ul><ul><li>Decomposes the underlying factors affecting the time series </li></ul></ul>
- 32. Bibliography & Readings List <ul><li>DeLurgio, Stephen, and Bhame, Carl. Forecasting Systems for Operations Management . Homewood: Business One Irwin, 1991. </li></ul><ul><li>Shim, Jae K. Strategic Business Forecasting . New York: St Lucie, 2000. </li></ul><ul><li>StatSoft Inc. (2003). Time Series Analysis. Retrieved April 21, 2003, from http://www.statsoft.com/textbook/sttimser.html </li></ul>
- 33. Appendix A: Exercise Templates
- 34. Appendix A: Exercise Templates
- 35. Appendix A: Exercise Templates
- 36. Appendix A: Exercise Templates
- 37. Appendix A: Exercise Templates
- 38. Appendix B: Exercise Solutions
- 39. Appendix B: Exercise Solutions
- 40. Appendix B: Exercise Solutions
- 41. Appendix B: Exercise Solutions Trend-cyclical Regression Equation T t = 5.402 + 0.514t
- 42. Appendix B: Exercise Solutions

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment