1. 12-1Forecasting CHAPTER 12 Forecasting AHNAF ABBAS Management Mathematics-76.

2. 12-2Forecasting CHAPTER 12 Objectives AHNAF ABBAS Management Mathematics-76. 1.How to Classify Forecasts 2.How to Calculate Moving Averages 3.How to Perform Exponential Smoothing.

3. 12-3Forecasting FORECAST:  A statement about the future value of a variable of interest such as demand.  Forecasts affect decisions and activities throughout an organization  Accounting, finance  Human resources  Marketing  MIS  Operations  Product / service design

4. 12-4Forecasting AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy MISIT/IS systems, services OperationsSchedules, workloads Product/service designNew products and services Uses of Forecasts

5. 12-5Forecasting  Assumes causal system past ==> future Past patterns (behavior) will continue into future.  Forecasts rarely perfect because of randomness  Forecast accuracy decreases as time horizon increases I see that you will get an A this semester. JOSHIJOSHI Basic Assumptions

6. 12-6Forecasting Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use

7. 12-7Forecasting Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Gather and analyze data Step 5 Prepare the forecast Step 6 Monitor the forecast “The forecast”

8. 12-8Forecasting Naive Forecasts Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell.... The forecast for any period equals the previous period’s actual value.

9. 12-9Forecasting  Simple to use  Virtually no cost  Quick and easy to prepare  Data analysis is nonexistent  Easily understandable  Cannot provide high accuracy Naïve Forecasts

10. 12-10Forecasting Types of Forecasts Types By lead time The time between when the forecast is made and the future point to which it refers.  Long-term: more than 10 years.  Medium-term: up to 5 years.  short-term: months to a year.

11. 12-11Forecasting Types of Forecasts  Univariate :Using past patterns e.g. Time series which uses historical data assuming the future will be like the past.  Multivariate- uses explanatory variables to predict the future, i.e. Past relationships between multiple variables.  Qualitative Judgmental - uses subjective inputs

12. 12-12Forecasting Judgmental Forecasts (Qualitative)  Executive opinions  Sales force opinions  Consumer surveys  Outside opinion  Delphi method  Opinions of managers and staff

13. 12-13Forecasting Time Series Forecasts  A time series is a continuous set of observations that are ordered in equally spaced intervals(e.g one per month).  Basic concept of univariate forecasting: Future values = f( Past values ) e.g. Two months average sales : Forecast for June = (April sales + May sales ) / 2 Univariate methods includes smoothing (averages) and exponential smoothing.

14. 12-14Forecasting Multivariate Forecasts  Known as Causal methods: make projections of the future by modeling the relationship between a series and other series. e.g. A forecast for furniture sales may be based on a relationship between economic indicators such as housing starts, personal income,No. of new marriages etc… : Future values = f( Past values, Values of other variables ) e.g. June demand = 50 + 0.2 MS + 1xAPI +0.5NH Multivariate methods include multiple regression and econometric.

15. 12-15Forecasting

16. 12-16Forecasting We’ll guess same as last month

17. 12-17Forecasting

18. 12-18Forecasting We’ll guess same as last month plus a little more for a possible trend

19. 12-19Forecasting This is easy, who needs forecasting

20. 12-20Forecasting Continue with our successful method: guess the same as last month plus a little more for a possible trend

21. 12-21Forecasting

22. 12-22Forecasting Definitely looks like a trend

23. 12-23Forecasting

24. 12-24Forecasting Trend might be a tad steeper than I thought

25. 12-25Forecasting Opps

26. 12-26Forecasting Momentary deviation, trend will continue

27. 12-27Forecasting See, I told you this was easy!

28. 12-28Forecasting Trend will continue

29. 12-29Forecasting Opps, another momentary fluctuation:

30. 12-30Forecasting Trend should continue

31. 12-31Forecasting Oh oh!

32. 12-32Forecasting Sales has leveled off: Lets average last few points

33. 12-33Forecasting Oh oh, maybe things are going down hill

34. 12-34Forecasting Let’s be conservative and Assume a negative trend

35. 12-35Forecasting Thank goodness, we are still basically level

36. 12-36Forecasting We’ll guess same as last month

37. 12-37Forecasting This stuff is easy

38. 12-38Forecasting We have for sure leveled off

39. 12-39Forecasting Big trouble!!! Chief forecaster Joshi and CEO Joshi1 fired!

40. 12-40Forecasting New chief forecaster points out the obvious trend

41. 12-41Forecasting Remarkable turnaround in sales. New CEO Joshi2 given credit

42. 12-42Forecasting Still looks like a trend to me

43. 12-43Forecasting Maybe not!

44. 12-44Forecasting Level except for anomaly

45. 12-45Forecasting Have things turned around?

46. 12-46Forecasting I’ll hedge my bets

47. 12-47Forecasting Things have turned around. Perhaps Joshi2 truly is a genius

48. 12-48Forecasting Trend up!

49. 12-49Forecasting Not bad!

50. 12-50Forecasting Revise trend a tad

51. 12-51Forecasting Joshi2 makes cover of Fortune Joshi1 Joshi2

52. 12-52Forecasting This is easy!!

53. 12-53Forecasting No big deal, trend continues (in an unrelated matter Joshi2 cashes out stock options)

54. 12-54Forecasting

55. 12-55Forecasting Heads will surely roll soon

56. 12-56Forecasting Let’s be cautiously optimistic

57. 12-57Forecasting Joshi2 called before board

58. 12-58Forecasting

59. 12-59Forecasting Perhaps we over reacted

60. 12-60Forecasting We will guess level

61. 12-61Forecasting Back to normal!

62. 12-62Forecasting

63. 12-63Forecasting Joshi2 fired!

64. 12-64Forecasting Structure of a Time Series  Trend patterns- general increase or decrease in a time series that lasts for certain period. population changes,changes in economic conditions..  Seasonality – results from the events that are periodic.Common seasonal influences : climate,human habits,holidays,….  Cycle – wavelike variations of more than one year’s duration. economic and business expansions,contractions.  Random variations - caused by chance,many influences that act independently to yield non repeating patterns.

65. 12-65Forecasting Forecast Variations Trend Irregular variatio n Seasonal variations 90 89 88 Figure 3.1 Cycles

66. 12-66Forecasting  Importance of Pattern : Actual value = Pattern + Error  Predicting values using Mean, Median or Mode  Mean : arithmetic average,measures that value about which 50% of deviations are above and 50% are below.i.e. Sum(Deviations) = 0 e.g. Time t = 1 2 3 4 5 6 7 (seven months) Value X=11 4 5 12 9 2 6; X = sales Mean Sales = 7 Sum(Deviations) = 0 Statistical Fundamentals 4 Forecasting

67. 12-67Forecasting  The Median : 50% of values are above and 50% are below. e.g. 2 4 5 6 9 11 12 Median = 6 When an even number of observations exists, Median = mean of middle two values.  The Mode : is the number or group of numbers that occur most often. Statistical Fundamentals 4 Forecasting

68. 12-68Forecasting  Comparison of Measures:  The Mean : Because it is the center of deviations, the mean is greatly influenced by the extreme values. e.g. A very large deviation (Outlier) will greatly affect the value of the mean. It is not appropriate without adjusting the outlier. The Median : is not affected by extreme values. Useful in describing highly skewed data. The Mode: is not affected by extremes. Statistical Fundamentals 4 Forecasting

69. 12-69Forecasting Example: Consider this sales time series for forecasting Period 9 : Period t = 1 2 3 4 5 6 7 8 Value X = 100 70 90 110 1200 110 130 80 Mean = 236.25 ; Median = 105 ; Mode = 110. Best estimate = 130 ; Mean = 102.5 ; Median = 105 ; Mode = 110 &130 Statistical Fundamentals 4 Forecasting

70. 12-70Forecasting Statistical Fundamentals 4 Forecasting Measuring Errors-Standard deviation & MAD Standard Deviation: The square root of the mean of the squared deviations. For a population : (RMS) Known as Root Mean Square Error For a Sample:

71. 12-71Forecasting Statistical Fundamentals 4 Forecasting Mean Absolute Deviation - MAD MAD = Comparison of Error Measures: MAD and Standard deviation are equivalent measures of dispersion. Despite the popularity of MAD, standard deviation is the preferred measure in forecasting.The more high the RMS& MAD,the better the Forecast.

72. 12-72Forecasting Univariate Methods  Moving average  Weighted moving average  Exponential smoothing Are effective methods for short term forecasts (series that do not have cyclical or seasonal patterns)

73. 12-73Forecasting Univariate Methods-Moving Averages  Moving averages: Future value will equal an average of past values.  Useful in random series because it averages or smoothes the most recent actual values to remove the unwanted randomness.  Remember : Forecast error = Actual - Forecast

74. 12-74Forecasting Univariate Methods-Moving Averages Example: Month t Actual MA 2 Error MA 4 Error Jan 1 120 Feb 2 124 Mar 3 122 122 0.00 April 4 123 123 0.00 May 5 125 122.5 2.50 122.25 2.75 Jun 6 128 124 4.00 123.5 4.50 Jul 7 129 126.5 2.5 124.5 4.50 Aug 8 127 128.5 -1.5 126.5 0.75

75. 12-75Forecasting Techniques for Averaging 1. Each new forecast moves ahead one period by adding the newest actual and dropping the oldest actual. MA 4 (May) = (Jan+Feb+Mar+Apr)/4 MA 4 (Jun) = (Feb+Mar+Apr+May)/4 2. Response to Recent data: MA’s Forecasts can be made less responsive to recent data by increasing the number of past observations. MA’s Forecasts can be made more responsive to recent data by decreasing the number of past observations.

76. 12-76Forecasting Simple Moving Average MA n = n AiAi i = 1  n Actual MA3 MA5

77. 12-77Forecasting Weighted Moving Averages  Weight 0.10 0.20 0.30 0.40  Month 1 2 3 4_ 5  Sales 100 90 105 95 ?  F5 = 0.40(95) + 0.30(105) + 0.20(90) + 0.10(100) = 97.5 units

78. 12-78Forecasting Exponential Smoothing  Smoothing constant determines the weight given to the most recent observations, it controls the rate of smoothing or averaging. F t = Exponentially smoothed forecast for period t. A t -1 = Actual in the prior period. F t -1 = Exponentially smoothed forecast of the prior period = Smoothing constant. ( 0 < < 1)

79. 12-79Forecasting Exponential Smoothing Example: suppose a company desires to forecast demand for a product with = 0.3. Last month’s actual = 1000 and the forecast was 900, the forecast for this month: F t = (0.3)(1000) + (1-0.3)(900) = 930 Alpha provides the relative weight given to each term of the equation. With alpha = 0.3,the forecast is 30% of the most recent Actual and 70% of the most recent Forecasted value.

80. 12-80Forecasting Forecast Accuracy  The fitted region is where we assume the data is known and we fit the model to this data.  The forecast region is where we assume the data is not known and has to be forecast using the model derived from the fitted region.  Mean Absolute Deviation (MAD)  Average absolute error  Mean Squared Error (MSE)  Average of squared error  Mean Absolute Percent Error (MAPE)  Average absolute percent error

81. 12-81Forecasting MAD, MSE, and MAPE MAD = Actualforecast   n MSE = Actualforecast ) 2   n-1 ( MAPE = Actualforecas t  n / Actual*100) 

82. 12-82Forecasting Absolute Error Measures e t = A t - F t  Month Actual Forec. Error. |Error| Error 2 St. Dev.  Jan. 10 15 -5 5 25 6.25  Feb. 12 14 -2 2 4 4.38  Mar. 14 13.6 0.4 0.4 0.16 3.09  Apr. 13 13.68 -0.68 0.68 0.46 2.53 49 56.28 -7.28 8.08 29.62 ME : mean error = = -1.82; MAD = = 0.5 SSE : sum of square errors = = 29.62

83. 12-83Forecasting Exponential Smoothing Steps in Using Exponential smoothing: 1. Choice of a smoothing constant:The best alphas should be chosen on the basis of Minimal sum of squared errors. 2. An initial forecast: the first actual value is chosen as the forecast for the second period. Example : Period Actual Forecast =0.3 1 900 2 1000 900 F 3 = A 2 +(1 - )F 2 = (0.3)(1000) + (1 -0.3)(900)=930

84. 12-84Forecasting Example - Exponential Smoothing

85. 12-85Forecasting Picking a Smoothing Constant .1 .4 Actual

86. 12-86Forecasting Example

87. 12-87Forecasting The Smoothing Constant 1. The weights of the past Actuals are determined by alpha: Most recent : One period old : Two periods old : etc… 2. The alpha that yields the most accurate forecast is the one that achieves the lowest MSE.

88. 12-88Forecasting The Smoothing Constant 3. If = 1,then F t = A t – 1 (zero smoothing) 4. Relation with number of periods : e.g. N = 19, then Useful when converting from or to MA’s Response to recent data: More responsive : higher alpha. Less responsive : lower alpha.

89. 12-89Forecasting Exercises

90. 12-90Forecasting Exercises

91. 12-91Forecasting Exercises