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## Forecasting

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**1. **Forecasting

**2. **What is Forecasting?

**3. **Short-range forecast
Up to 1 year (usually less than 3 months)
Job scheduling, worker assignments
Medium-range forecast
3 months to 3 years
Sales & production planning, budgeting
Long-range forecast
3 years, or more
New product planning, facility location Forecasts by Time Horizon At this point, it may be useful to point out the “time horizons” considered by different industries. For example, some colleges and universities look 30 to fifty years ahead, industries engaged in long distance transportation (steam ship, railroad) or provision of basic power (electrical and gas utilities, etc.) also look far ahead (20 to 100 years). Ask them to give examples of industries having much shorter long-range horizons.At this point, it may be useful to point out the “time horizons” considered by different industries. For example, some colleges and universities look 30 to fifty years ahead, industries engaged in long distance transportation (steam ship, railroad) or provision of basic power (electrical and gas utilities, etc.) also look far ahead (20 to 100 years). Ask them to give examples of industries having much shorter long-range horizons.

**4. **Long vs. Short Term Forecasting Long and Medium range forecasts
deal with more comprehensive issues
support management decisions regarding planning and products, plants and processes.
Short-term forecasts
usually employ different methodologies than longer-term forecasting
tend to be more accurate than longer-term forecasts. At this point it may be helpful to discuss the actual variables one might wish to forecast in the various time periods.At this point it may be helpful to discuss the actual variables one might wish to forecast in the various time periods.

**5. **Influence of Product Life Cycle Stages of introduction and growth require longer forecasts than maturity and decline
Forecasts useful in projecting
Staffing levels,
Inventory levels, and
Factory capacity
as product passes through life cycle stages This slide introduces the impact of product life cycle on forecasting The following slide, reproduced from chapter 2, summarizes the changing issues over the product’s lifetime for those faculty who wish to treat the issue in greater depth.This slide introduces the impact of product life cycle on forecasting The following slide, reproduced from chapter 2, summarizes the changing issues over the product’s lifetime for those faculty who wish to treat the issue in greater depth.

**6. **Types of Forecasts Economic forecasts
Address the business cycle (e.g., inflation rate, money supply, etc.)
Technological forecasts
Predict the rate of technological progress
Predict acceptance of new products
Demand forecasts
Predict sales of existing products One can use an example based upon one’s college or university. Students can be asked why each of these forecast types is important to the college. Once they begin to appreciate the importance, one can then begin to discuss the problems. For example, is predicting “demand” merely as simple as predicting the number of students who will graduate from high school next year (i.e., a simple counting exercise)?One can use an example based upon one’s college or university. Students can be asked why each of these forecast types is important to the college. Once they begin to appreciate the importance, one can then begin to discuss the problems. For example, is predicting “demand” merely as simple as predicting the number of students who will graduate from high school next year (i.e., a simple counting exercise)?

**7. **Seven Steps in Forecasting Determine the use of the forecast
Select the items to be forecasted
Determine the time horizon of the forecast
Select the forecasting model(s)
Gather the data
Make the forecast
Validate and implement results A point to be made here is that one requires a forecasting “plan,” not merely the selection of a particular forecasting methodology.A point to be made here is that one requires a forecasting “plan,” not merely the selection of a particular forecasting methodology.

**8. **Realities of Forecasting Forecasts are seldom perfect
Most forecasting methods assume that there is some underlying stability in the system
Both product family and aggregated product forecasts are more accurate than individual product forecasts This slide provides a framework for discussing some of the inherent difficulties in developing reliable forecasts. You may wish to include in this discussion the difficulties posed by attempting forecast in a continuously, and rapidly changing environment where product life-times are measured less often in years and more often in months than ever before.
One might wish to emphasize the inherent difficulties in developing reliable forecasts.This slide provides a framework for discussing some of the inherent difficulties in developing reliable forecasts. You may wish to include in this discussion the difficulties posed by attempting forecast in a continuously, and rapidly changing environment where product life-times are measured less often in years and more often in months than ever before.
One might wish to emphasize the inherent difficulties in developing reliable forecasts.

**9. **Forecasting Approaches This slide distinguishes between Quantitative and Qualitative forecasting. If you accept the argument that the future is one of perpetual, and perhaps significant change, you may wish to ask students to consider whether quantitative forecasting will ever be sufficient in the future - or will we always need to employ qualitative forecasting also. (Consider Tupperware’s ‘jury of executive opinion.’)This slide distinguishes between Quantitative and Qualitative forecasting. If you accept the argument that the future is one of perpetual, and perhaps significant change, you may wish to ask students to consider whether quantitative forecasting will ever be sufficient in the future - or will we always need to employ qualitative forecasting also. (Consider Tupperware’s ‘jury of executive opinion.’)

**10. **Forecasting Approaches …The reality of all forecasting techniques is that they depend on both subjective and objective inputs…
…That is to say that, regardless of the initial approach, all forecasting techniques are a blend of both art and science

**11. **Qualitative Methods Jury of executive opinion
Pool opinions of high-level executives, sometimes augment by statistical models
Delphi method
Panel of experts, queried iteratively
Sales force composite
Estimates from individual salespersons are reviewed for reasonableness, then aggregated
Consumer Market Survey
Ask the customer This slide outlines several qualitative methods of forecasting. Ask students to give examples of occasions when each might be appropriate.
The next several slides elaborate on these qualitative methods.This slide outlines several qualitative methods of forecasting. Ask students to give examples of occasions when each might be appropriate.
The next several slides elaborate on these qualitative methods.

**12. **Jury of Executive Opinion Ask your students to consider other potential disadvantages. (Politics?)Ask your students to consider other potential disadvantages. (Politics?)

**13. **Sales Force Composite You might ask your students to consider what problems might occur when trying to use this method to predict sales of a potential new product.You might ask your students to consider what problems might occur when trying to use this method to predict sales of a potential new product.

**14. **Delphi Method Iterative group process
3 types of people
Decision makers
Staff
Respondents
Reduces ‘group-think’ You might ask your students to consider whether there are special examples where this technique is required. ( Questions of technology transfer or assessment, for example; or other questions where information from many different disciplines is required.)You might ask your students to consider whether there are special examples where this technique is required. ( Questions of technology transfer or assessment, for example; or other questions where information from many different disciplines is required.)

**15. **Consumer Market Survey You might discuss some of the difficulties with this technique. Certainly there is the issue that what consumers say is often not what they do. There are other problems such as that consumers sometime wish to please the surveyor; and for unusual, future, products, consumers may have a very imperfect frame of reference within which to consider the question.You might discuss some of the difficulties with this technique. Certainly there is the issue that what consumers say is often not what they do. There are other problems such as that consumers sometime wish to please the surveyor; and for unusual, future, products, consumers may have a very imperfect frame of reference within which to consider the question.

**16. **Quantitative Approaches Naïve approach
Moving average
Weighted moving average
Exponential smoothing
Exponential smoothing with trend
Trend projection
Seasonally adjusted

**17. ** Set of evenly spaced numerical data
Obtained by observing response variable at regular time periods
Forecast based only on past values
Assumes that factors influencing past and present will continue influence in future
Example
Year: 1998 1999 2000 2001 2002
Sales: 78.7 63.5 89.7 93.2 92.1 Time Series Models This and subsequent slide frame a discussion on time series - and introduce the various components.This and subsequent slide frame a discussion on time series - and introduce the various components.

**18. **Any observed value in a time series is the product (or sum) of time series components
Multiplicative model:
Yi = Ti · Si · Ci · Ri
Additive model:
Yi = Ti + Si + Ci + Ri Time Series Methods This slide introduces two general forms of time series model. You might provide examples of when one or the other is most appropriate.This slide introduces two general forms of time series model. You might provide examples of when one or the other is most appropriate.

**19. **Time Series Terms Stationary Data
a time series variable exhibiting no significant upward or downward trend over time
Nonstationary Data
a time series variable exhibiting a significant upward or downward trend over time
Seasonal Data
a time series variable exhibiting a repeating patterns at regular intervals over time

**20. **Time Series Components

**21. **Persistent, overall upward or downward pattern
Due to population, technology etc.
Several years duration Trend Component

**22. **Regular pattern of up & down fluctuations
Due to weather, customs, etc.
Occurs within 1 year Seasonal Component

**23. **Repeating up & down movements
Due to interactions of factors influencing economy
Can be anywhere between 2-30+ years duration Cyclical Component

**24. **Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events
Union strike
Tornado
Short duration & non-repeating Random Component

**25. **Demand with Trend & Seasonality This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor?This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor?

**26. **Time Series Analysis There are many, many different time series techniques
It is usually impossible to know which technique will be best for a particular data set
It is customary to try out several different techniques and select the one that seems to work best
To be an effective time series modeler, you need to keep several time series techniques in your “tool box”

**27. **Naive Approach This slide introduces the naïve approach. Subsequent slides introduce other methodologies.This slide introduces the naïve approach. Subsequent slides introduce other methodologies.

**28. **Naïve Example

**29. **Naïve Forecast

**30. **Naïve Forecast Chart

**31. ** MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing
Provides overall impression of data over time
Equation: Moving Average Method At this point, you might discuss the impact of the number of periods included in the calculation. The more periods you include, the closer you come to the overall average; the fewer, the closer you come to the value in the previous period. What is the tradeoff?At this point, you might discuss the impact of the number of periods included in the calculation. The more periods you include, the closer you come to the overall average; the fewer, the closer you come to the value in the previous period. What is the tradeoff?

**32. **3 period MA Example

**33. **3 period MA Forecast

**34. **3 period MA Forecast Chart

**35. **Older data may be considered less important as a predictor
Weights based on intuition
May be established as any numerical value
Equation: Weighted Moving Average Method This slide introduces the “weighted moving average” method. It is probably most important to discuss choice of the weights.This slide introduces the “weighted moving average” method. It is probably most important to discuss choice of the weights.

**36. **3 period WMA Example

**37. **3 period WMA Forecast

**38. **3 period WMA Forecast Chart

**39. **Increasing n makes forecast less sensitive to changes
Do not forecast trend well
Require a great amount of historical data
Only account for random variation Disadvantages of MA Methods These points should have been brought out in the example, but can be summarized here.These points should have been brought out in the example, but can be summarized here.

**40. **Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant (?)
Ranges: 0 < ? < 1
Subjectively chosen
The larger the value of ?, the more responsive the model will be to historical data Exponential Smoothing Method This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows.This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows.

**41. **Ft = ?At - 1 + ?(1-?)At - 2 + ?(1- ?)2·At - 3 + ?(1- ?)3At - 4 + ... + ?(1- ?)t-1·A0
Ft = Forecast value
At = Actual value
? = Smoothing constant
Ft = Ft-1 + ?(At-1 - Ft-1)
Use for computing forecast
If F1 is unknown, then F1 = A1 Exponential Smoothing Equations You may wish to discuss several points:
- this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time.
- the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point.
- we need a formal process and criteria for choosing the “best” smoothing constant.You may wish to discuss several points:
- this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time.
- the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point.
- we need a formal process and criteria for choosing the “best” smoothing constant.

**42. **ES Example (? = 0.1)

**43. **ES Forecast (? = 0.1)

**44. **ES Forecast (? = 0.1) Chart

**45. **ES Example (? = 0.5)

**46. **ES Forecast (? = 0.5)

**47. **ES Forecast (? = 0.5) Chart

**48. **Which Model Is “Best” So Far? Naïve = 20
3MA = 17.33
3WMA = 18.9
ES (a = 0.1) = 14.83
ES (a = 0.5) = 18.36

**49. **Exponential Smoothing with Trend Adjustment This slide introduces exponential smoothing with trend adjustment. The equations and additional material follow.This slide introduces exponential smoothing with trend adjustment. The equations and additional material follow.

**50. **Exponential Smoothing with Trend Adjustment - continued

**51. **Ft = exponentially smoothed forecast of the data series in period
If F1 is unknown, then F1 = A1
Tt = exponentially smoothed trend in period t
If T1 is unknown, then T1 = 0
At = actual demand in period t
? = smoothing constant for the average
Ranges: 0 < ? < 1
? = smoothing constant for the trend
Ranges: 0 < ? < 1 Exponential Smoothing with Trend Adjustment - continued

**52. **Used for forecasting linear trend line
Assumes relationship between response variable, Y, and time, X, is a linear function
Estimated by least squares method
Minimizes sum of squared errors Linear Trend Projection This slide introduces the equation produced in linear trend progression. This slide introduces the equation produced in linear trend progression.

**53. **Least Squares This slide introduces the topic of least squares.
One might try to make the point, using this slide, that the goal of least squares is to minimize the average deviation without regard to the mathematical sign of the deviation. The average of the deviations could be minimized by making their sum equal to zero - but we could still be left with large positive and negative deviations. Minimizing the sum of the square of the deviations produces a more “balanced” set of deviations.This slide introduces the topic of least squares.
One might try to make the point, using this slide, that the goal of least squares is to minimize the average deviation without regard to the mathematical sign of the deviation. The average of the deviations could be minimized by making their sum equal to zero - but we could still be left with large positive and negative deviations. Minimizing the sum of the square of the deviations produces a more “balanced” set of deviations.

**54. **Linear Trend Forecast Chart

**55. **Linear Trend Equations Again, this is basically a repeat of the slide for the linear trend problem.Again, this is basically a repeat of the slide for the linear trend problem.

**56. **Slope (b)
Estimated Y changes by b for each 1 unit increase in X
If b = 2, then sales (Y) is expected to increase by 2 for each 1 unit increase in advertising (X)
Y-intercept (a)
Average value of Y when X = 0
If a = 4, then average sales (Y) is expected to be 4 when advertising (X) is 0 Interpretation of Coefficients This slide probably merits discussion - additional to that for the linear trend model.
You might make the point here that the dependent and independent variable are not necessarily of the same nature - they need not both be dollars, for example.
You might also wish to note that setting x = 0 may not have a useful physical interpretation.This slide probably merits discussion - additional to that for the linear trend model.
You might make the point here that the dependent and independent variable are not necessarily of the same nature - they need not both be dollars, for example.
You might also wish to note that setting x = 0 may not have a useful physical interpretation.

**57. **Variation of actual Y from predicted Y
Measured by standard error of estimate
Sample standard deviation of errors
Denoted SY,X
Affects several factors
Parameter significance
Prediction accuracy Random Error Variation Here you may wish to at least begin the discussion of the distinction between explainable and unexplainable, and random and non-random error variation. There are also slides which come later in the presentation that will refer to this topic.Here you may wish to at least begin the discussion of the distinction between explainable and unexplainable, and random and non-random error variation. There are also slides which come later in the presentation that will refer to this topic.

**58. **Least Squares Assumptions Relationship is assumed to be linear. Plot the data first - if curve appears to be present, use curvilinear analysis.
Relationship is assumed to hold only within or slightly outside data range. Do not attempt to predict time periods far beyond the range of the data base.
Deviations around least squares line are assumed to be random. This slide raises several points:
- What does it mean to be “linear”? How does one tell if something is linear or not? Or perhaps, how does one tell if something is sufficiently linear that a linear regression model is appropriate?
- If the relationship is assumed to hold only within or slightly outside the data range, how do we use this model to make projections into the future (for which we don’t have data)?
- What does it mean for data to be random? How can we tell? You might discuss making scatter plots not only of the original data, but also of the resulting deviations. (Obviously there are more rigorous methods of determining if the deviations are random, but a scatter plot is a good start.)This slide raises several points:
- What does it mean to be “linear”? How does one tell if something is linear or not? Or perhaps, how does one tell if something is sufficiently linear that a linear regression model is appropriate?
- If the relationship is assumed to hold only within or slightly outside the data range, how do we use this model to make projections into the future (for which we don’t have data)?
- What does it mean for data to be random? How can we tell? You might discuss making scatter plots not only of the original data, but also of the resulting deviations. (Obviously there are more rigorous methods of determining if the deviations are random, but a scatter plot is a good start.)

**59. **Answers: ‘how strong is the linear relationship between the variables?’
Coefficient of correlation Sample correlation coefficient denoted r
Range: -1 < r < 1
Measures degree of association
Used mainly for understanding Correlation This slide can frame the start of a discussion of correlation.. You should probably expect to add to this a discussion of cause and effect, emphasizing in particular that correlation does not imply a cause and effect relationship. Ask student to suggest examples of significant correlation of unrelated phenomenon.This slide can frame the start of a discussion of correlation.. You should probably expect to add to this a discussion of cause and effect, emphasizing in particular that correlation does not imply a cause and effect relationship. Ask student to suggest examples of significant correlation of unrelated phenomenon.

**60. **Coefficient of Correlation (r) This slide presents additional examples of the meaning of the correlation coefficient.This slide presents additional examples of the meaning of the correlation coefficient.

**61. **Additive vs. Multiplicative Seasonality

**62. ** An Additive Seasonal Model Et is the expected level at time period t.
St is the seasonal factor for time period t.

**63. **A Multiplicative Seasonal Model Et is the expected level at time period t.
St is the seasonal factor for time period t.

**64. **Multiplicative Example (p. 124) Find average historical demand for each “season” by summing the demand for that season in each year, and dividing by the number of years for which you have data.
Compute the average demand over all seasons by dividing the total average annual demand by the number of seasons.
Compute a seasonal index by dividing that season’s historical demand (from step 1) by the average demand over all seasons.
Estimate next year’s total demand
Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season. This provides the seasonal forecast. This slide provides a quick view of the development of a multiplicative seasonal model.This slide provides a quick view of the development of a multiplicative seasonal model.

**65. **Seasonal Example (p. 124)

**66. **You want to achieve:
No pattern or direction in forecast error
Error = (Yi - Yi) = (Actual - Forecast)
Seen in plots of errors over time
Smallest forecast error
Mean Absolute Deviation (MAD), or Mean Absolute Percentage Error (MAPE)
Mean Squared Error (MSE) Selecting a Forecasting Model This slide introduces overall guideline for selecting a forecasting model. You may also wish to re-emphasize the role of scatter plots, and discuss the role of “understanding what is going on” (especially in limiting one’s choice of model).This slide introduces overall guideline for selecting a forecasting model. You may also wish to re-emphasize the role of scatter plots, and discuss the role of “understanding what is going on” (especially in limiting one’s choice of model).

**67. **Mean Square Error (MSE)
Mean Absolute Deviation (MAD)
Mean Absolute Percent Error (MAPE) Forecast Error Equations This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.

**68. **Naïve Forecast Errors

**69. **3MA Forecast Errors

**70. **3 WMA Forecast Errors

**71. **ES (? = 0.1) Forecast Errors

**72. **ES (? = 0.5) Forecast Errors

**73. **Which Model Is “Best” So Far? The Naïve model has both the lowest MAD (1.91) and MSE (4.45) of the first five models tested
Therefore, the Naïve model is the “best”
However, it may be that one model has the lowest MAD or MAPE and another model has the lowest MSE…

**74. **So Which Model Do You Choose? If you only require the forecast with the smallest average deviation, choose the model with the smallest MAD or MAPE
However, if you have a low tolerance for large deviations choose the model with the smallest MSE

**75. **Control Charts for Forecasting Once you have selected the “best” forecasting model… construct a control chart to monitor the continuing performance of the model’s forecasts:
The center line is the average error = 0
The upper and lower control limits use a proxy of (+ or – 2 times the root mean square error) to approximate a
95% level of confidence.

**76. **Control Charts for Forecasting

**77. **Control Charts for Forecasting Once you have constructed the chart plot each new forecast error and examine the trend for any patterns…
If any patterns develop there is “cause for inspection”
…making the existing model suspect and
The parameters might need modification, or
A new model must be developed

**78. **Patterns in Control Charts Ask the students to imagine a product, and consider what problem might cause each of the graph configurations illustrated.Ask the students to imagine a product, and consider what problem might cause each of the graph configurations illustrated.

**79. **Forecasting Quiz Suppose you had the following sales:
Use the models:
4MA
3WMA [3, 2, 1]
ES [alpha = 0.1]
ES [alpha = 0.5]
Forecast period 13 for each
Find the MAD & MSE for each
Answers…