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Forecasting

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Published in: Physics
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Sandeep K / Kolkata

3 years of teaching experience

Qualification: M.Tech. (Production Engineering)

Teaches: Chemistry, English, Hindi, Physics, Drawing, Mechanical

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  1. Forecasting
  2. HOW MANY BUSINESS CARDS SHOULD ORDER? 8 1 USE A COnPLEX FORMULA BASED ON YOUR BURN RATE AND YOUR LIKELIHOOO OF GETTING DOWN- SIZED e: 1 USE ABOUT THREE PER WEEK YOIJLL NEED THREE CARDS 1 Copur i gh t DEPENDS. 28B.3 Lini ted Feature Sund i eate, Ine
  3. Objectives ' Give the fundamental rules of forecasting ' Calculate a forecast using a moving average, weighted moving average, and exponential smoothing ' Calculate the accuracy of a forecast
  4. What is forecasting? Forecasting is a tool used for predicting future demand based on past demand information.
  5. Why is forecasting important? Demand for products and services is usually uncertain. Forecasting can be used for... Strategic planning (long range planning) Finance and accounting (budgets and cost controls) Marketing (future sales, new products) Production and operations
  6. What is forecasting all about? Demand for Mercedes E Class Time Jan Feb Mar Apr May Jun Jul Aug O Actual demand (past sales) o Predicted demand We try to predict the future by looking back at the past Predicted demand looking back six months
  7. What's Forecasting All About? From the March 10, 2006 WSJ: Ahead of the Oscars, an economics professor, at the request of Weekend Journal, processed data about this year's films nominated for best picture through his statistical model and predicted with 97.4% certainty that "Brokeback Mountain" would win. Oops. Last year, the professor tuned his model until it correctly predicted 18 of the previous 20 best-picture awards; then it predicted that "The Aviator" would win; "Million Dollar Baby" won instead. Sometimes models tuned to prior results don't have great predictive powers.
  8. Some general characteristics of forecasts Forecasts are always wrong Forecasts are more accurate for groups or families of items Forecasts are more accurate for shorter time periods Every forecast should include an error estimate Forecasts are no substitute for calculated demand.
  9. Key issues in forecasting 1. 2. A forecast is only as good as the information included in the forecast (past data) History is not a perfect predictor of the future (i.e.: there is no such thing as a perfect forecast) REMEMBER: Forecasting is based on the assumption that the past predicts the future! When forecasting, think carefully whether or not the past is strongly related to what you expect to see in the future...
  10. Example: Mercedes E-class vs. M-class Sales Month Jan Feb Mar Apr May Jun Jul E-class Sales 23,345 22,034 21,453 24,897 23,561 22,684 M-class Sales Question: Can we predict the new model M-class sales based on the data in the the table? Answer: Maybe... We need to consider how much the two markets have in common
  11. What should we consider when looking at past demand data? Trends Seasonality Cyclical elements Autocorrelation Random variation
  12. Some Important Questions What is the purpose of the forecast? Which systems will use the forecast? ' How important is the past in estimating the future? Answers will help determine time horizons, techniques, and level of detail for the forecast.
  13. Types of forecasting methods Qualitative methods Rely on subjective opinions from one or more experts. Quantitative methods Rely on data and analytical techniques.
  14. Qualitative forecasting methods Grass Roots: deriving future demand by asking the person closest to the customer. Market Research: trying to identify customer habits; new product ideas. Panel Consensus: deriving future estimations from the synergy of a panel of experts in the area. Historical Analogy: identifying another similar market. Delphi Method: similar to the panel consensus but with concealed identities.
  15. Quantitative forecasting methods Time Series: models that predict future demand based on past history trends Causal Relationship: models that use statistical techniques to establish relationships between various items and demand Simulation: models that can incorporate some randomness and non-linear effects
  16. How should we pick our forecasting model? l. 2. 3. 4. Data availability Time horizon for the forecast Required accuracy Required Resources
  17. Time Series: Moving average The moving average model uses the last t periods in order to predict demand in period t+ 1. There can be two types of moving average models: simple moving average and weighted moving average The moving average model assumption is that the most accurate prediction of future demand is a simple (linear) combination of past demand.
  18. Time series: simple moving average In the simple moving average models the forecast value is t n A At + Atl + ... + A t-n is the current period. is the forecast for next period is the forecasting horizon (how far back we look), is the actual sales figure from each period.
  19. Example: forecasting sales at Kroger Kroger sells (among other stuff) bottled spring water Month Jan Feb Mar Apr May Jun Jul Bottles 1,325 1,353 What will 1,305 the sales be 1,275 for July? 1,210 1,195 '2
  20. What if we use a 3-month simple moving average? A Jun + A May + A Apr Jul = 1,227 What if we use a 5-month simple moving average? A Jun + A May + A Apr + A Mar + A Feb = 1,268 Jul
  21. 1400 1350 1300 1250 1200 1150 1100 1050 I OOO 1 2 3 4 5 6 7 5 -month MA forecast 3 -month MA forecast 8 What do we observe? 5-month average smoothes data more; 3-month average more responsive
  22. Stability versus responsiveness in moving averages 1000 900 800 700 600 500 I Demand 3-\/Veek 2 3 4 5 678 Week 9 10 Il 12
  23. Time series: weighted moving average We may want to give more importance to some of the data... Wt At + Wt_l At 1 + W t + Wt_l + + W is the current period. t-n t-n t n A w is the forecast for next period is the forecasting horizon (how far back we look), is the actual sales figure from each period. is the importance (weight) we give to each period
  24. Why do we need the W MA models? Because of the ability to give more importance to what happened recently, without losing the impact of the past. Demand for Mercedes E-class Jan Feb Mar Apr May Jun Jul Aug O Actual demand (past sales) Prediction when using 6-month SMA Prediction when using 6-months W MA Time For a 6-month SMA, attributing equal weights to all past data we miss the downward trend
  25. Example: Kroger sales of bottled water Month Jan Feb Mar Apr May Jun Jul Bottles 1,325 1,353 1,305 1,275 1,210 1,195 '2 What will be the sales for July?
  26. 6-month simple moving average. , . A Jun + A May + A Apr + A Mar + A Feb + A Jan = 1,277 Jul In other words, because we used equal weights, a slight downward trend that actually exists is not observed...
  27. What if we use a weighted moving average? Make the weights for the last three months more than the first three months... 6-month SMA July 1,277 Forecast WMA 1,267 WMA 1,257 WMA 1,247 The higher the importance we give to recent data, the more we pick up the declining trend in our forecast.
  28. How do we choose weights? 1. 2. Depending on the importance that we feel past data has Depending on known seasonality (weights of past data can also be zero). WMA is better than SMA because of the ability to vary the weights!
  29. Time Series: Exponential Smoothing (ES) Main idea: The prediction of the future depends mostly on the most recent observation, and on the error for the latest forecast. Smoothin constant alpha a Denotes the importance of the past error
  30. Why use exponential smoothing? 1. 2. 3. 4. 5. Uses less storage space for data Extremely accurate Easy to understand Little calculation complexity There are simple accuracy tests
  31. Exponential smoothing: the method Assume that we are currently in period t. We calculated the forecast for the last period (Ft_l) and we know the actual demand last period (At 1) ... The smoothing constant a expresses how much our forecast will react to observed differences... If a is low: there is little reaction to differences. If a is high: there is a lot of reaction to differences.
  32. Example: bottled water at Kroger u = 0.2 Month Jan Feb Mar Apr May Jun Actual 1,325 1,353 1,305 1,275 1,210 Forecasted 1,370 1,361 1,359 1 , 309
  33. Example: bottled water at Kroger u = 0.8 Month Jan Feb Mar Apr May Jun Actual 1,325 1,353 1,305 1,275 1,210 Forecasted 1,370 1,283 1,225
  34. Impact of the smoothing constant 1380 1360 1340 1320 1300 1280 1260 1240 1220 1200 0 Actual a = 0.2 a = 0.8 1 2 3 4 5 6 7
  35. Trend.. What do you think will happen to a moving average or exponential smoothing model when there is a trend in the data?
  36. Impact of trend Sales Actual Data Forecast Regular exponential smoothing will always lag behind the trend. Can we include trend analysis in exponential smoothing? Month
  37. Exponential smoothing with trend FITt=Ft+Tt = FIT +a(At FIT: Forecast including trend ö: Trend smoothing constant -FIT l) -FIT l) The idea is that the two effects are decoupled, (F is the forecast without trend and T is the trend component)
  38. Example: bottled water at Kroger 0.8 0.5 Jan Feb Mar Apr May Jun 1325 1353 1305 1275 1210 1380 1334 1344 1311 1278 1218 -10 -28 -9 -21 — 27 -43 FITt 1370 1306 1334 1290 1251 1175
  39. Exponential Smoothing with Trend 1400 1 350 1300 1 250 1 200 1150 Actual a = 0.2 a = 0.8 0.8, d = 0.5 1 2 3 4 5 6 7
  40. Linear regression in forecasting Linear regression is based on 1. Fitting a straight line to data 2. Explaining the change in one variable through changes in other variables. dependent variable = a + b x (independent variable) By using linear regression, we are trying to explore which independent variables affect the dependent variable
  41. Example: do people drink more when it's cold? Alcohol Sales Which line best fits the data? Average Monthly Temperature
  42. The best line is the one that minimizes the error The predicted line is So, the error is ... Where: e y Y is the error is the observed value is the predicted value
  43. Least Squares Method of Linear Regression The goal of LSM is to minimize the sum of squared errors... Min 2
  44. What does that mean? Alcohol Sales so LSM tries to minimize the distance between the line and the points ! Average Monthly Temperature
  45. Least Squares Method of Linear Regression Then the line is defined by 2 x —2
  46. How can we compare across forecasting models? We need a metric that provides estimation of accuracy Forecast Error Errors can be: 1. biased (consistent) 2. random Forecast error = Difference between actual and forecasted value (also known as residual)
  47. Measuring Accuracy: MFE MFE = Mean Forecast Error (Bias) It is the average error in the observations E At-Ft i=l MFE = 1. A more positive or negative MFE implies worse performance; the forecast is biased.
  48. Measuring Accuracy: MAD MAD = Mean Absolute Deviation It is the average absolute error in the observations MAD E At-Ft i=l 1. Higher MAD implies worse performance. 2. If errors are normally distributed, then 0€=1.25MAD
  49. MFE & MAD: A Dartboard Analogy Low MFE & MAD: 4) The forecast errors are small & unbiased
  50. An Analogy (cont'd) Low MFE but high MAD: On average, the arrows hit the bullseye (so much for averages ! )
  51. MFE & MAD: An Analogy High MFE & MAD: The forecasts are inaccurate & biased
  52. Key Point Forecast must be measured for accuracy! The most common means of doing so is by measuring the either the mean absolute deviation or the standard deviation of the forecast error
  53. Measuring Accuracy: Tracking signal The tracking signal is a measure of how often our estimations have been above or below the actual value. It is used to decide when to re-evaluate using a model. RSFE ) RSFE MAD Positive tracking signal: most of the time actual values are above our forecasted values Negative tracking signal: most of the time actual values are below our forecasted values If TS > 4 or < -4, investigate!
  54. Example: bottled water at Kroger Month Jan Feb Mar Apr May Jun Actual 1,325 1,353 1,305 1,275 1,210 1,195 Forecast 1,370 1,361 1,359 1,349 1,334 1,309 Month Jan Feb Mar Apr May Jun Actual 1,325 1,353 1,305 1,275 1,210 1,195 Forecast 1370 1306 1334 1290 1251 1175 Exponential Smoothing (u = 0.2) Forecasting with trend (u = 0.8) (b = 0.5) Question: Which one is better?
  55. Bottled water at Kroger: compare MAD and TS MAD Exponential 70 Smoothing Forecast 33 Including Trend - 6.0 - 2.0 We observe that FIT performs a lot better than ES Conclusion: Probably there is trend in the data which Exponential smoothing cannot capture
  56. Which Forecasting Method Should You Use ' Gather the historical data of what you want to forecast Divide data into initiation set and evaluation set Use the first set to develop the models Use the second set to evaluate Compare the MADs and MFEs of each model

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