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1. Business Forecasting A Hands-On Course

2. Agenda

3. Picturing Distributions www.learner.org/resources/series65.html Professor Theresa Amabile Brandeis University

4. Types of Forecasting Methods Judgmental Methods Extrapolative Methods Explanatory (cause and effect) Methods The Case of New Product Forecasting

5. Judgmental Forecasting Quantitative techniques using the power of the computer have come to dominate the forecasting landscape. However, there is a rich history of forecasting based on subjective or judgmental methods, most of which remain useful today. These methods are probably most appropriately used when the forecaster is faced with a severe shortage of historical data and/or when quantitative expertise is not available.

6. Judgmental Forecasting Very long-range forecasting is an example of such a situation requiring judgmental forecasting. The computer-based quantitative models that are the focal point of this workshop have less applicability to such things as forecasting the type of home entertainment that will be available 40 years from now than do those methods based on expert judgments. 

7. Judgmental Methods

8. Sales Force Composite The sales force can be a rich source of information about future trends and changes in buyer behavior. Members of the sales force are asked to estimate sales for each product they handle. These estimates are usually based on each individual’s subjective “feel” for the level of sales that would be reasonable in the forecast period. This process takes advantage of information from sources very close to actual buyers.

9. Surveys In some situations it may be practical to survey customers for advanced information about their buying intentions. This practice presumes that buyers plan their purchases and follow through with their plans. The SRC (Univ. of Michigan) produces an Index of Consumer Sentiment (ICS) based on a survey of 500 individuals, 40 percent of whom are respondents who participated in the survey six months earlier and the remaining 60 percent are new respondents selected on a random basis.

10. Jury of Executive Opinion The judgments of experts in any area are a valuable resource. A forecast is developed by combining the subjective opinions of the managers and executives who are most likely to have the best insights about the firm’s business. the forecaster may collect opinions in individual interviews or in a meeting where the participants have an opportunity to discuss various points of view.

11. Delphi Method Six Steps: Participating panel members are selected. Questionnaires asking for opinions about the variables to be forecast are distributed to panel members. Results from panel members are collected, tabulated, and summarized. Summary results are distributed to the panel members for their review and consideration. 5. Panel members revise their individual estimates, taking account of the information received from the other, unknown panel members. 6. Steps 3 through 5 are repeated until no signi?cant changes result.

12. Why Use Judgmental Methods? Requires no quantitative skills. Captures some forces that cannot be replicated in quantitative models. Can be used to improve (not replace) quantitative methods.

13. Some Forecasting Publications Journal of Business Forecasting International Journal of Forecasting Journal of Forecasting

15. Two Naïve Models 1) Forecast value is equal to the previous observed value. 2) Forecast value is equal to the previous observed value plus a proportion of the most recently observed rate of change in the variable.

16. Civilian Unemployment Rate

17. Civilian Unemployment Rate

18. First Naïve Forecasting Model

19. First Naïve Forecast

20. Second Naïve Forecast In addition to considering the most recent observation, it might make sense to consider the direction from which we arrived at the most recent observation.

21. Second Naïve Forecast

22. Second Naïve Forecast

23. Evaluating Forecast Accuracy

24. Root Mean Square Error

25. Calculation of RMSE

26. Seven Accuracy Measures

27. Seven Accuracy Measures ME and MPE are not often used because of large positive errors can be offset by large negative errors. They are, however, good measures of bias. The other measures are best used to compare alternative forecasting models for a given series. Because of different units used for various series, only MAPE and Theil’s U should be interpreted across series (e.g., for comparing a series of percentages with a series measured in units).

28. Seven Accuracy Measures

29. Theil’s U-statistic Theil’s U-statistic is a special type of error measure somewhat unlike MAPE and RMSE. The measure compares the accuracy of the forecast model to that of a “naïve” competitor. It is the ratio of the standard error of the model to the 1-step ahead standard error of the naive model.

30. “Out Of Sample” To determine how accurate models are in actual forecasts, a holdout period is often used.

31. Combining Forecasts Simply

32. Forecasting Domestic Car Sales

33. Forecasting Gap Sales

34. Agenda

35. Moving Average Method Simple moving averages may mimic some data better than more complicated functions. A moving average is a series of numbers obtained by overlapping groups of two or more consecutive values in a time series. The average is “moving” because an ever-new average is calculated by adding a more recent time series value to the group and dropping the oldest one.

36. Moving Averages Be careful of the Slutsky - Yule Effect Moving averages produce misleading patterns of points over an extended period of time; it creates periodicities where there are none in the original data Moving averages produce a pattern over an extended period of time. Moving Averages create periodicities where there are none in the original data.

37. Slutsky-Yule Effect

38. Slutsky-Yule Effect

39. Slutsky–Yule Effect The reason for the waves is simple. Consider a set of random numbers: The original numbers vary randomly Any sum of these will fluctuate. When the sum is high, there are more larger than smaller numbers. Chances are lower that a larger number will be added next than a lower number will be added next. But a large number will be dropped, so the sum and average will decline.

40. Moving Average Method

41. Moving Average Method

42. Moving Average Method

44. Moving Average Method

45. Simple Exponential Smoothing The simple exponential smoothing model can be written in the following manner: F t+1 = ? X t + ( 1 - ?) F t where: F t+1 = forecasted value for next period ???The smoothing constant (0< ?<1) X t = Actual value of time series now (in period t) F t = Forecasted (i.e. smoothed) value for time period t

46. Weights for Alpha = .1 Time Calculation Weight for Xt t .1 t-1 .9 X .1 .090 t-2 .9 X .9 X .1 .081 t-3 .9 X .9 X .9 X .1 .073 . . . ------------------------------------------------------- Total = 1.000

47. Weights for Alpha = .9 Time Calculation Weight for Xt t .9 t-1 .1 X .9 .09 t-2 .1 X .1 X .9 .009 t-3 .1 X .1 X .1 X .9 .0009 . . . ----------------------------------------------------------- Total = 1.000

48. Family of Smoothing Models

49. Simple Exponential Smoothing Pros Requires a limited amount of data Relatively simple compared to other forecasting methods Cons Its forecasts lag behind the actual data Has no ability to adjust for any trend or seasonality

50. Rule of Thumb In actual practice, alpha values from 0.05 to 0.30 work very well in most simple smoothing models. If a value of greater than 0.30 gives the best RMSE this usually indicates that another forecasting technique would work even better.

52. Index of Consumer Sentiment

53. Holt’s Exponential Smoothing Used for data exhibiting some trend over time Is just as simple to apply as simple smoothing Involves two smoothing factors, a simple smoothing factor and a trend smoothing factor

54. Holt’s Exponential Smoothing

55. Holt’s Exponential Smoothing

56. 1970 Draft Lottery Was a trend exhibited in the data? Moving Average (i.e., running median trace) Double Holt’s Exponential Smoothing

57. Holt Winter’s Ex. Smoothing Adjusts for both trend and seasonality Is just as simple to apply as simple smoothing Involves the use of three smoothing parameters, a simple smoothing parameter, a trend smoothing parameter and a seasonality smoothing parameter

58. Holt Winter’s Ex. Smoothing

59. Holt Winter’s Ex. Smoothing

60. Houses Sold Data Hourly Earnings Data Holt Winter’s Ex. Smoothing

61. Another Method for Seasonality Calculate the seasonal index for the series Deseasonalize the raw data Apply the forecasting method Reseasonalize the series

62. What is a Seasonal Index?

63. What is a Seasonal Index?

64. What is a Seasonal Index?

65. What is a Seasonal Index?

66. Interpreting the Seasonal Index?

67. Interpreting the Seasonal Index?

73. Intermittent Demand - Croston Croston’s Approach Used to handle sporadic data Demand is often zero, sometimes not Uses two pieces of information Demand size Demand Occurrence Attempts to provide an optimal safety stock

75. Intermittent Demand - Slow Slow Moving Demand Crostons assumes a normal distribution Slow Moving Method assumes seasonality Calculates an optimal stocking level

77. Automatic Model Selection Neural Network Limited number of methods Simple decision rules Usually user selectable

78. New Product Forecasting

92. People in collectivist cultures care more about what others think of them and seem to react accordingly. In countries with higher purchasing power, the p tends to be higher. More disposable income makes it easier to adopt innovations; the p tends to be higher. Products that exhibit significant network effects or require heavy investment in complimentary infrastructure (like television and the cellular telephone) will have higher values for q.

100. Time Series Decomposition

128. Appliance Store Sales/Real Auto Sales The Gap

138. Rewriting The Equation

139. The Problem

140. The Minimization Problem

141. The Intercept and Slope

142. Retail Sales Model

143. Four Quick Checks

144. First Quick Check

145. Second Quick Check

146. t-Distribution

147. A Bad Regression

148. Third Quick Check

149. Third Quick Check

150. Fourth Quick Check

151. Fourth Quick Check

152. Fourth Quick Check

153. The Durbin Watson statistic may be used to check for any order of serial correlation. Quarterly data will normally be subject to 4th order serial correlation. Monthly data will more likely be subject to 12th order serial correlation.

154. How To Get Rid of Autocorrelation

155. Confidence Interval

156. Confidence Interval

157. Confidence Interval

158. Growth Models - Nonlinearities Linear Growth Increases/decreases by constant amount Exponential Growth Increases/decreases by constant percentage See “Against All Odds”#7

159. Multiple Regression Model

160. Multiple Regression Model

161. Multiple Regression Model

162. Multiple Regression Model

163. Multiple Regression Model R2

164. Multicollinearity

165. Multicollinearity

166. F-Statistic

167. The F-Statistic is a “Test of the Overall Significance of a Multiple Regression. The F-Statistic is also explained as a “Joint Test of Significance” because it test the significance of all the coefficients at the same time. N.B. The t-tests and the F-test are different!

200. Identification

212. Seasonal ARIMA Model

219. Three Step Process Check to see if the combined regression (with a constant term) has an insignificant constant term. Run the same regression WITHOUT a constant term. Combine the forecasts with the optimal weights.

223. Progress Diagram

224. Table

225. 3-D Pie Chart

226. Marketing Diagram