# Forecasting Models

Topics: Forecasting, Regression analysis, Exponential smoothing Pages: 27 (7162 words) Published: February 12, 2013
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C H A P T E R

Forecasting Models

5

TEACHING SUGGESTIONS
Teaching Suggestion 5.1: Wide Use of Forecasting. Forecasting is one of the most important tools a student can master because every ﬁrm needs to conduct forecasts. It’s useful to motivate students with the idea that obscure sounding techniques such as exponential smoothing are actually widely used in business, and a good manager is expected to understand forecasting. Regression is commonly accepted as a tool in economic and legal cases. Teaching Suggestion 5.2: Forecasting as an Art and a Science. Forecasting is as much an art as a science. Students should understand that qualitative analysis (judgmental modeling) plays an important role in predicting the future since not every factor can be quantiﬁed. Sometimes the best forecast is done by seat-of-thepants methods. Teaching Suggestion 5.3: Use of Simple Models. Many managers want to know what goes on behind the forecast. They may feel uncomfortable with complex statistical models with too many variables. They also need to feel a part of the process. Teaching Suggestion 5.4: Management Input to the Exponential Smoothing Model. One of the strengths of exponential smoothing is that it allows decision makers to input constants that give weight to recent data. Most managers want to feel a part of the modeling process and appreciate the opportunity to provide input. Teaching Suggestion 5.5: Wide Use of Adaptive Models. With today’s dominant use of computers in forecasting, it is possible for a program to constantly track the accuracy of a model’s forecast. It’s important to understand that a program can automatically select the best alpha and beta weights in exponential smoothing. Even if a ﬁrm has 10,000 products, the constants can be selected very quickly and easily without human intervention. Week 1 2 3 4 5 6 7

Actual Bicycle Sales 8 10 9 11 10 13 —

Three-Week Moving Average

(8 10 9)/3 (10 9 11)/3 (9 11 10)/3 (11 10 13)/3

9 10 10 11Z\c

Alternative Example 5.2: Weighted moving average ) ∑ (weight for period n)(demand in period n) ∑ weights Bower’s Bikes decides to forecast bicycle sales by weighting the past 3 weeks as follows: Weights Applied 3 2 1 6 Period Last week Two weeks ago Three weeks ago Sum of weights

A 3-week weighted moving average appears below.
Actual Bicycle Sales 8 10 9 11 10 13 —

Week 1 2 3 4 5 6 7

Three-Week Moving Average

[(3 9) (2 10) (1 8)]/6 [(3 11) (2 9) (1 10)]/6 [(3 10) (2 11) (1 9)]/6 [(3 13) (2 10) (1 11)]/6

9Z\n 10Z\n 10Z\n 11X\c

ALTERNATIVE EXAMPLES
Alternative Example 5.1: ∑ demand in previous n periods Moving average = n Bicycle sales at Bower’s Bikes are shown in the middle column of the following table. A 3-week moving average appears on the right.

Alternative Example 5.3: A ﬁrm uses simple exponential smoothing with a 0.1 to forecast demand. The forecast for the week of January 1 was 500 units, whereas actual demand turned out to be 450 units. The demand forecasted for the week of January 8 is calculated as follows. Ft 1

Ft 500

α(At 0.1(450

Ft) 500) 495 units

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CHAPTER 5

FORECASTING MODELS

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Alternative Example 5.4: Exponential smoothing is used to forecast automobile battery sales. Two values of are examined, 0.8 and 0.5. To evaluate the accuracy of each smoothing constant, we can compute the absolute deviations and MADs. Assume that the forecast for January was 22 batteries. Absolute Deviation with 0.8 Absolute Deviation with 0.5 2 0 6 4 3 31.5 16.5 2.75

Month January February March April May June

Actual Battery Sales 20 21 15 14 13 16

Forecast with 0.8

Forecast with 0.5 22 21 21 18 16 14.5

22 2 20.40 0.6 20.880 5.88 16.176 2.176 14.435 1.435 13.287 2.713 Sum of absolute deviations: 15 MAD: 2.46

On the basis of this analysis, a smoothing constant of preferred to 0.5...