Time Series and Trend Analysis

1. Time Series and Trend Analysis

2. Time Series and Trend Analysis • Definition • Main Components of Time Series • Measurement of the Underlying Trend • Seasonal Data movement

3. Definition • Time series examines a series of data over time. In studying the series, patterns become evident and these past patterns are used to assist with future decision making.

4. Main Components of Time Series • Secular Trend • Seasonal Variation • Cyclical Fluctuations • Irregular Movements

5. Measurement of the Underlying Trend • Freehand graphic method • Moving average • Exponential smoothing • Semi-average • Least-squares method

6. 1. Moving Average (odd)

7. 1. Moving Average (even)

8. 2. Exponential Smoothing Sx = Y + (1- )Sx-1  = (0 - 1)

9.  =0.4

10. Predict for 2010 Sx = Y + (1- )Sx-1 = 14,000 ×0.4 +(1-0.4) ×13107.2 = 13,464.32

11. 3. Semi-averaging Method y = a + bt

12. Semi-averaging Method y ∑ (y - yt) = 0

13. Semi-averaging Method

14. yt= a + bt

16. ∑ (y - yt) = 0 yt= a + bt ∑ [ y - ( a + bt) ] = 0 ∑ y - ∑(a+bt) = 0 ∑ y – na - b∑t = 0 ∑ y – na - b∑t = 0

17. 4. Least Squares Method

18. Least Squares Method y ∑ (y - yt)2 = min

19. Correlation

22. = 18.3 + 1.03t

23. = 18.3 + 1.03t • Please predict sales for 2011. t=6 = 18.3 + 1.03×6 = 22.48

24. Seasonal Data Movement 1,467.19 1,394.49 1,141.99 1,516.55

25. Seasonal Data Movement 101.35 91.79 95.36 110.25