Topic 5: FORECASTING

1. Topic 5: FORECASTING

2. I. Introduction -- What is forecasting? • Scientific (educated) guess • Based on past data or experience • Rarely perfect • Group forecast more accurate • Shorter time horizon, more accurate -- Why forecasting?

3. -- Forecasting time horizon • Short range – usually less than 3 months • Medium range – 3 months to 3 years • Long range – over 3 years • * Related to the product life cycle

4. -- Which forecasting method to use? • Time horizon • Costs vs. accuracy • Easy to understand?

5. Irregularvariation Trend Cycles Several years -- Pattern of Data • Trend – gradual upward or downward movement • Cycle – background pattern over long period of time

6. Year 2 Year 1 Year 3 Seasonal variations -- Pattern of Data (continued) • Seasonality – repeated pattern • Randomness (irregular variation) – unexplainable, unpredictable, unknown fluctuations

7. II. Qualitative Forecasting Methods Qualitative Forecasting Methods- no past data is available, for managerial decision, long term forecast • Jury of executive opinion • Method of combining and averaging views of several executives regarding a specific decision or forecast. • Drawback: one person’s view may prevail

8. Qualitative Forecasting Methods • The Delphi technique – systematic survey of experts • Collaborative estimating or forecasting technique that combines independent analysis with maximum use of feedback, for building consensus among experts who interact anonymously. • Drawback: expensive and time consuming

9. Qualitative Forecasting Methods • Sales force composite • A method of developing a sales forecast that uses the opinions of each member of the field sales staff regarding how much the individual expects to sell in the period as input. • Drawback: Overly influenced by recent experiences

10. Qualitative Forecasting Methods • Consumer market survey • The gathering and evaluation regarding consumers' preferences for products and services • Drawback: like to do will do

11. III. Quantitative Forecasting Methods • Time series data: a sequence of data points, measured typically at successive times, spaced at (often uniform) time intervals

12. Quantitative Forecasting Methods • Smoothing Techniques: for time series data with no clear pattern, short term forecast • Naïve:estimating technique in which the last period's actual is used as this period's forecast, without adjusting them or attempting to establish causal factors. • It is used only for comparison with the forecasts generated by the better (sophisticated) techniques.

13. Quantitative Forecasting Methods (Smoothing Techniques) • n Period Moving Average (MA-n): arithmetical average n most recent period real observations as the forecast for next time period.

14. Quantitative Forecasting Methods (Smoothing Techniques) • n Period Weighted Moving Average (WMA-n): flexible weight assignment • For n most recent observations , assign flexible weights of , respectively Forecast for next time period t +1 is

15. Quantitative Forecasting Methods (Smoothing Techniques) • Exponential Smoothing with smoothing constant : very little data record required, more weight on recent data, weight decreases exponentially

16. Quantitative Forecasting Methods (Smoothing Techniques) • Example: Forecast the score for test 5 by the above smoothing techniques For exponential smoothing, use a = 0.1 and F1 = 77.

17. Quantitative Forecasting Methods (Smoothing Techniques) • Relationship between smoothing techniques • average of past data, but differ in weight distribution • all methods lag behind actual data change • more weight on most recent data, more responsive, less smooth

18. Quantitative Forecasting Methods (Smoothing Techniques) • Thinking challenge: • Which method requires the least amount of data? • What happens if the a in the exponential smoothing method increases?

19. Quantitative Forecasting Methods (Trend Projection by Linear Regression) • Trend Projection by Linear Regression • for data with linear trend pattern, medium term • Step 1. Find a trend line to fit the past data the best (minimizing mean squared errors) • best slope:

20. Quantitative Forecasting Methods (Trend Projection by Linear Regression) • best intercept: and are the average of x’s and y’s. • * Excel commands: • calculating b:“=slope(range of y’s, range of x’s)” • calculating a:“=intercept(range of y’s, range of x’s)”

21. Quantitative Forecasting Methods (Trend Projection by Linear Regression) • Example continued:

22. Quantitative Forecasting Methods (Trend Projection by Linear Regression) • Step 2. Trend projection • Trend projection forecast: • -- Example continues:

23. Quantitative Forecasting Methods (Trend Projection by Linear Regression) • Step 3. Find forecast interval, if necessary • Forecast interval = • standard error • * Excel commands: calculating :”=steyx(range of y’s, range of x’s)” • Example continues:

24. Quantitative Forecasting Methods(Causal Model by Linear Regression) • Causal Model by Linear Regression: same set up as trend projection, except that x is an independent variable (other than time), y is a dependent variable, medium term

25. Quantitative Forecasting Methods(Causal Model by Linear Regression) • Example: The sales manager of a large apartment rental complex feels the demand for apartments may be related to the number of newspaper ads placed during the previous month. She has collected the data shown below. If the number of ads placed in this month is 30, what would be her estimate of rentals in the coming month?

26. Quantitative Forecasting Methods(Causal Model by Linear Regression) • Correlation coefficient r: measures the strength of linear relationship between x and y • * Excel command: calculating r:”=correl(range of y’s, range of x’s)”

27. Quantitative Forecasting Methods(Causal Model by Linear Regression) • -- Interpretation: • r > 0: • r = 0: • r < 0: • = coefficient of determination: % of variation in the dependent variable (y) is explained by regression equation (linear relationship). • Example continued: How strong is the relationship between the ads placed and the rentals?

28. Quantitative Forecasting Methods(Decomposition by Time Series) • Decomposition of Time Series -- for data with both trend and seasonality patterns, short to medium term • Idea: • Decompose the past data (filter out the seasonal influence from original data) • Forecast trend pattern and seasonality pattern separately • Combine the forecasts using the multiplicative model:

29. Quantitative Forecasting Methods(Decomposition by Time Series) • -- Example: Data of a popular brand of sweater sale (by quarters) over the past three years. Forecast the sale of each season in next year (Year 4).

30. Quantitative Forecasting Methods(Decomposition by Time Series) • Step 1. Draw the historical data diagram to check if there is an obvious seasonal pattern

31. Quantitative Forecasting Methods(Decomposition by Time Series) • Step 2. Calculate the "seasonal indexes" (S) (quarter relatives) for each season. • Seasonal Index = Avg. Seasonal Sale / Total Avg Sale

32. Quantitative Forecasting Methods(Decomposition by Time Series) • Step 3. Deseasonalize the original data:

33. Quantitative Forecasting Methods(Decomposition by Time Series)

34. Quantitative Forecasting Methods(Decomposition by Time Series)

35. Quantitative Forecasting Methods(Decomposition by Time Series) • Step 4. Calculate the trend based on the deseasonalized demand by linear regression

36. Quantitative Forecasting Methods(Decomposition by Time Series) • Step 5. Use trend projection to forecast the demand with trend only. T13 = T14 = T15 = T16 =

37. Quantitative Forecasting Methods(Decomposition by Time Series) • Step 6. Use seasonal indexes to modify the forecasts to reflect the seasonality patterns: F13 = F14 = F15 = F16 =

38. Quantitative Forecasting Methods(Decomposition by Time Series)

39. Quantitative Forecasting Methods(Decomposition by Time Series)

40. IV. Choosing a Forecasting Method • Choosing a Forecasting Method - all criteria are a function of the forecast error • forecast error (E) = actual realization (Y)– forecast (F)

41. Choosing a Forecasting Method • Bias – measures the direction of forecast • Bias = ( forecast error) / n

42. Choosing a Forecasting Method • Mean Absolute Deviation (MAD) - same penalty for small and large errors MAD = ( |forecast error|) / n

43. Choosing a Forecasting Method • Mean Squared Error (MSE) • – more penalty on large errors • MSE = ( (forecast error)2 )/n

44. Choosing a Forecasting Method • Mean Absolute Percent Error (MAPE) • relative error, scale independent • MAPE = (  |forecast error|/Actual Data) / n

45. Choosing a Forecasting Method • Comparing different forecasting methods • Based on past performance • Measure dependent • Choose  (for exp. Smoothing) and n (for MA) to minimize MAD, MSE, or MAPE

46. Choosing a Forecasting Method • Example: Same data as earlier • Bias • MAD • MSE • MAPE

47. Choosing a Forecasting Method

48. V. Control of the Forecasting Process • Control of the Forecasting Process - to check if the performance of a forecasting method changes

49. Control of the Forecasting Process • Tracking Signal control chart: • plotting statistic TS(t) = RSFE(t) / MAD(t) • RSFE(t) = running sum of the forecast error through time t • MAD(t) = MAD through time t • 3 sigma control chart limits: UCL = 3, LCL = -3, CL = 0

50. Control of the Forecasting Process • -- Interpretation?