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Classical Decomposition

Classical Decomposition. Boise State University By: Kurt Folke Spring 2003. Overview:. Time series models & classical decomposition Brainstorming exercise Classical decomposition explained Classical decomposition illustration Exercise Summary Bibliography & readings list

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Classical Decomposition

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  1. Classical Decomposition Boise State University By: Kurt Folke Spring 2003

  2. Overview: • Time series models & classical decomposition • Brainstorming exercise • Classical decomposition explained • Classical decomposition illustration • Exercise • Summary • Bibliography & readings list • Appendix A: exercise templates

  3. Time Series Models & Classical Decomposition • Time series models are sequences of data that follow non-random orders • Examples of time series data: • Sales • Costs • Time series models are composed of trend, seasonal, cyclical, and random influences

  4. Time Series Models & Classical Decomposition • Decomposition time series models: • Multiplicative: Y = T x C x S x e • Additive: Y = T + C + S + e • T = Trend component • C = Cyclical component • S = Seasonal component • e = Error or random component

  5. Time Series Models & Classical Decomposition • Classical decomposition is used to isolate trend, seasonal, and other variability components from a time series model • Benefits: • Shows fluctuations in trend • Provides insight to underlying factors affecting the time series

  6. Brainstorming Exercise • Identify how this tool can be used in your organization…

  7. Classical Decomposition Explained Basic Steps: • Determine seasonal indexes using the ratio to moving average method • Deseasonalize the data • Develop the trend-cyclical regression equation using deseasonalized data • Multiply the forecasted trend values by their seasonal indexes to create a more accurate forecast

  8. Classical Decomposition Explained: Step 1 • Determine seasonal indexes • Start with multiplicative model… Y = TCSe • Equate… Se = (Y/TC)

  9. Classical Decomposition Explained: Step 1 • To find seasonal indexes, first estimate trend-cyclical components Se = (Y/TC) • Use centered moving average • Called ratio to moving average method • For quarterly data, use four-quarter moving average • Averages seasonal influences Example

  10. Classical Decomposition Explained: Step 1 • Four-quarter moving average will position average at… • end of second period and • beginning of third period • Use centered moving average to position data in middle of the period Example

  11. Classical Decomposition Explained: Step 1 • Find seasonal-error components by dividing original data by trend-cyclical components Se = (Y/TC) • Se = Seasonal-error components • Y = Original data value • TC = Trend-cyclical components (centered moving average value) Example

  12. Classical Decomposition Explained: Step 1 • Unadjusted seasonal indexes (USI) are found by averagingseasonal-error components by period • Develop adjusting factor (AF) so USIs are adjusted so their sum equals the number of quarters (4) • Reduces error Example Example

  13. Classical Decomposition Explained: Step 1 • Adjusted seasonal indexes (ASI) are derived by multiplying the unadjusted seasonal index by the adjusting factor ASI = USI x AF • ASI = Adjusted seasonal index • USI = Unadjusted seasonal index • AF = Adjusting factor Example

  14. Classical Decomposition Explained: Step 2 • Deseasonalized data is produced by dividing the original data values by their seasonal indexes (Y/S) = TCe • Y/S = Deseasonalized data • TCe = Trend-cyclical-error component Example

  15. Classical Decomposition Explained: Step 3 • Develop the trend-cyclical regression equation using deseasonalized data Tt = a + bt • Tt = Trend value at period t • a = Intercept value • b = Slope of trend line Example

  16. Classical Decomposition Explained: Step 4 • Use trend-cyclical regression equation to develop trend data • Create forecasted data by multiplying the trend data values by their seasonal indexes • More accurate forecast Example Example

  17. Classical Decomposition Explained: Step Summary Summarized Steps: • Determine seasonal indexes • Deseasonalize the data • Develop the trend-cyclical regression equation • Create forecast using trend data and seasonal indexes

  18. Classical Decomposition:Illustration • Gem Company’s operations department has been asked to deseasonalize and forecast sales for the next four quarters of the coming year • The Company has compiled its past sales data in Table 1 • An illustration using classical decomposition will follow

  19. Classical Decomposition Illustration: Step 1 • (a) Compute the four-quarter simple moving average Ex: simple MA at end of Qtr 2 and beginning of Qtr 3 (55+47+65+70)/4 = 59.25 Explain

  20. Classical DecompositionIllustration: Step 1 • (b) Compute the two-quarter centered moving average Ex: centered MA at middle of Qtr 3 (59.25+61.25)/2 = 60.500 Explain

  21. Classical Decomposition Illustration: Step 1 • (c) Compute the seasonal-error component (percent MA) Ex: percent MA at Qtr 3 (65/60.500) = 1.074 Explain

  22. Classical DecompositionIllustration: Step 1 • (d) Compute the unadjusted seasonal index using the seasonal-error components from Table 2 Ex (Qtr 1): [(Yr 2, Qtr 1) + (Yr 3, Qtr 1) + (Yr 4, Qtr 1)]/3 = [0.989+0.914+0.926]/3 = 0.943 Explain

  23. Classical DecompositionIllustration: Step 1 • (e) Compute the adjusting factor by dividing the number of quarters (4) by the sum of all calculated unadjusted seasonal indexes = 4.000/(0.943+0.851+1.080+1.130) = (4.000/4.004) Explain

  24. Classical DecompositionIllustration: Step 1 • (f) Compute the adjusted seasonal index by multiplying the unadjusted seasonal index by the adjusting factor Ex (Qtr 1): 0.943 x (4.000/4.004) = 0.942 Explain

  25. Classical DecompositionIllustration: Step 2 • Compute the deseasonalized sales by dividing original sales by the adjusted seasonal index Ex (Yr 1, Qtr 1): (55 / 0.942) = 58.386 Explain

  26. Classical DecompositionIllustration: Step 3 • Compute the trend-cyclical regression equation using simple linear regression Tt = a + bt t-bar = 8.5 T-bar = 69.6 b = 1.465 a = 57.180 Tt = 57.180 + 1.465t Explain

  27. Classical DecompositionIllustration: Step 4 • (a) Develop trend sales Tt = 57.180 + 1.465t Ex (Yr 1, Qtr 1): T1 = 57.180 + 1.465(1) = 58.645 Explain

  28. Classical DecompositionIllustration: Step 4 • (b) Forecast sales for each of the four quarters of the coming year Ex (Yr 5, Qtr 1): 0.942 x 82.085 = 77.324 Explain

  29. Classical DecompositionIllustration: Graphical Look

  30. Classical Decomposition:Exercise • 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 • Use the steps and examples shown in the explanation and illustration as a reference Basic Steps Explanation Illustration Templates

  31. Summary • Time series models are sequences of data that follow non-arbitrary orders • Classical decomposition isolates the components of a time series model • Benefits: • Insight to fluctuations in trend • Decomposes the underlying factors affecting the time series

  32. Bibliography &Readings List DeLurgio, Stephen, and Bhame, Carl. Forecasting Systems for Operations Management. Homewood: Business One Irwin, 1991. Shim, Jae K. Strategic Business Forecasting. New York: St Lucie, 2000. StatSoft Inc. (2003). Time Series Analysis. Retrieved April 21, 2003, from http://www.statsoft.com/textbook/sttimser.html

  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

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