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Lecture 4: Trend and Seasonal Series

Lecture 4: Trend and Seasonal Series. Techniques for trend Techniques for seasonality Summary Readings: Page 79-92. Techniques for Trend. Linear Trend Equation. F t = Forecast for period t t = Specified number of time periods a = Value of F t at t = 0 b = Slope of the line.

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Lecture 4: Trend and Seasonal Series

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  1. Lecture 4: Trend and Seasonal Series • Techniques for trend • Techniques for seasonality • Summary • Readings: Page 79-92 ISMT/Stuart Zhu

  2. Techniques for Trend • Linear Trend Equation • Ft = Forecast for period t • t = Specified number of time periods • a = Value of Ft at t = 0 • b = Slope of the line ISMT/Stuart Zhu

  3. Sales Data for Five Weeks ISMT/Stuart Zhu

  4. y ∆y ∆t t 0 ISMT/Stuart Zhu

  5. Calculate a and b (1) (2) where n = number of periods, yi = value of the time series at time ti ISMT/Stuart Zhu

  6. Linear Trend Equation Example ISMT/Stuart Zhu

  7. 5 (2499) - 15(812) 12495 - 12180 b = = = 6.3 5(55) - 225 275 - 225 Linear Trend Calculation 812 - 6.3(15) a = = 143.5 5 y = 143.5 + 6.3t ISMT/Stuart Zhu

  8. Techniques for Seasonality • Seasonal variations • Regularly repeating movements in series values that can be tied to recurring events. ISMT/Stuart Zhu

  9. Seasonal variation Linear Trend x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 1 2 3 4 Year ISMT/Stuart Zhu

  10. Two Models • Additive model • Demand = Trend + Seasonality • Multiplicative model • Demand = Trend * Seasonality ISMT/Stuart Zhu

  11. Using Seasonal Relatives • Seasonal relative • Percentage of average or trend • Computing Seasonal relatives • Centered moving average: a moving average positioned at the center of the data ISMT/Stuart Zhu

  12. Example 7 at Page 84 Forecast-s3 • Compute estimated relatives for each day • Suppose that the trend equation is given by 120 +5t • Give Friday represents t=5, what is the forecast on Friday? ISMT/Stuart Zhu

  13. Summary • Compute the trend equation • a, b, • How to compute and use seasonal relatives ISMT/Stuart Zhu

  14. Review Problems • Problem 5 at page 113 • Problem 10 at page 115 • Problem 11 at page 115 • Problem 12 at page 115 ISMT/Stuart Zhu

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