probability and statistics
Joss_Smitx01
chap007_Nobels-3.pptMcGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 7
Introduction to Forecasting
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Forecasting
- Plays an important role in many industries
marketing
financial planning
production control
- Forecasts are not to be thought of as a final product but as a tool in making a managerial decision
7-*
Forecasting
- Forecasts can be obtained qualitatively or quantitatively
- Qualitative forecasts are usually the result of an expert’s opinion and is referred to as a judgmental technique
- Quantitative forecasts are usually the result of conventional statistical analysis
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Forecasting Components
- Time Frame
long term forecasts
short term forecasts
- Existence of patterns
seasonal trends
peak periods
- Number of variables
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Patterns in Forecasts
- Trend
A gradual long-term up or down movement of demand
Demand
Time
Upward Trend
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Patterns in Forecasts
- Cycle
An up and down repetitive movement in demand
Demand
Time
Cyclical Movement
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Quantitative Techniques
- Two widely used techniques
Time series analysis
Linear regression analysis
- Time series analysis studies the numerical values a variable takes over a period of time
- Linear regression analysis expresses the forecast variable as a mathematical function of other variables
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Time Series Analysis
- Latest Period Method
- Moving Averages
- Example Problem
- Weighted Moving Averages
- Exponential Smoothing
- Example Problem
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Latest Period Method
- Simplest method of forecasting
- Use demand for current period to predict demand in the next period
- e.g., 100 units this week, forecast 100 units next week
- If demand turned out to be only 90 units then the following weeks forecast will be 90
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Moving Averages
- Uses several values from the recent past to develop a forecast
- Tends to dampen or smooth out the random increases and decreases of a latest period forecast
- Good for stable demand with no pronounced behavioral patterns
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Moving Averages
- Moving averages are computed for specific periods
Three months
Five months
The longer the moving average the smoother the forecast
- Moving average formula
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Moving Averages - NASDAQ
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Weighted MA
- Allows certain demands to be more or less important than a regular MA
- Places relative weights on each of the period demands
- Weighted MA is computed as such
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Weighted MA
- Any desired weights can be assigned, but SWi=1
- Weighting recent demands higher allows the WMA to respond more quickly to demand changes
- The simple MA is a special case of the WMA with all weights equal, Wi=1/n
- The entire demand history is carried forward with each new computation
- However, the equation can become burdensome
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Exponential Smoothing
- Based on the idea that a new average can be computed from an old average and the most recent observed demand
- e.g., old average = 20, new demand = 24, then the new average will lie between 20 and 24
- Formally,
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Exponential Smoothing
- Note: a must lie between 0.0 and 1.0
- Larger values of a allow the forecast to be more responsive to recent demand
- Smaller values of a allow the forecast to respond more slowly and weights older data more
- 0.1 < a < 0.3 is usually recommended
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Exponential Smoothing
- The exponential smoothing form
- Rearranged, this form is as such
- This form indicates the new forecast is the old forecast plus a proportion of the error between the observed demand and the old forecast
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Why Exponential Smoothing?
- Continue with expansion of last expression
- As t>>0, we see (1-a)t appear and <<1
- The demand weights decrease exponentially
- All weights still add up to 1
- Exponential smoothing is also a special form of the weighted MA, with the weights decreasing exponentially over time
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Forecasting with Seasonality
- Calculate the average demand per season
e.g.: average quarterly demand
- Calculate a seasonal index for each season of each year:
Divide the actual demand of each season by the average demand per season for that year
- Average the indexes by season
e.g.: take the average of all Spring indexes, then of all Summer indexes, ...
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Forecasting with Seasonality
- Forecast demand for the next year & divide by the number of seasons
Use regular forecasting method & divide by four for average quarterly demand
- Multiply next year’s average seasonal demand by each average seasonal index
Result is a forecast of demand for each season of next year
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Forecast Error
- Error
- Cumulative Sum of Forecast Error
- Mean Square Error
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Forecast Error
- Mean Absolute Error
- Mean Absolute Percentage Error
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CFE
- Referred to as the bias of the forecast
- Ideally, the bias of a forecast would be zero
- Positive errors would balance with the negative errors
- However, sometimes forecasts are always low or always high (underestimate/overestimate)
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MSE and MAD
- Measurements of the variance in the forecast
- Both are widely used in forecasting
- Ease of use and understanding
- MSE tends to be used more and may be more familiar
- Link to variance and SD in statistics
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MAPE
- Normalizes the error calculations by computing percent error
- Allows comparison of forecasts errors for different time series data
- MAPE gives forecasters an accurate method of comparing errors
- Magnitude of data set is negated
MA
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CFE
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MSE
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MAPE
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