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Time Series and Trend Analysis. Time Series and Trend Analysis. Definition Main Components of Time Series Measurement of the Underlying Trend Seasonal Data movement. Definition.
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Time Series and Trend Analysis • Definition • Main Components of Time Series • Measurement of the Underlying Trend • Seasonal Data movement
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.
Main Components of Time Series • Secular Trend • Seasonal Variation • Cyclical Fluctuations • Irregular Movements
Measurement of the Underlying Trend • Freehand graphic method • Moving average • Exponential smoothing • Semi-average • Least-squares method
2. Exponential Smoothing Sx = Y + (1- )Sx-1 = (0 - 1)
Predict for 2010 Sx = Y + (1- )Sx-1 = 14,000 ×0.4 +(1-0.4) ×13107.2 = 13,464.32
3. Semi-averaging Method y = a + bt
Semi-averaging Method y ∑ (y - yt) = 0
∑ (y - yt) = 0 yt= a + bt ∑ [ y - ( a + bt) ] = 0 ∑ y - ∑(a+bt) = 0 ∑ y – na - b∑t = 0 ∑ y – na - b∑t = 0
Least Squares Method y ∑ (y - yt)2 = min
= 18.3 + 1.03t • Please predict sales for 2011. t=6 = 18.3 + 1.03×6 = 22.48
Seasonal Data Movement 1,467.19 1,394.49 1,141.99 1,516.55
Seasonal Data Movement 101.35 91.79 95.36 110.25