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Forecasting “Prediction is very difficult, especially if it's aboutthe future.” Nils Bohr 
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ObjectivesGive the fundamental rules of forecasting Calculate a forecast using a moving average, weighted moving average, and exponential smoothing Calculate the accuracy of a forecast 
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What is forecastingForecasting is a tool used for predicting future demand based on past demand information. 
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Why is forecasting importantDemand 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 
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What is forecasting all aboutWe try to predict the future by looking back at the past Actual demand (past sales) Predicted demand 
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What’s Forecasting All AboutFrom 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 bestpicture 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. 
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Some general characteristics of forecastsForecasts 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. 
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Key issues in forecastingA 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… 
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Example: Mercedes Eclass vsMclass Sales Question: Can we predict the new model Mclass sales based on the data in the the table? Answer: Maybe... We need to consider how much the two markets have in common Month Eclass Sales Mclass Sales Jan 23,345  Feb 22,034  Mar 21,453  Apr 24,897  May 23,561  Jun 22,684  Jul ? ? 
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What should we consider when looking at past demand dataTrends Seasonality Cyclical elements Autocorrelation Random variation 
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Some Important QuestionsWhat 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. 
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Types of forecasting methodsQualitative methods Quantitative methods Rely on subjective opinions from one or more experts. Rely on data and analytical techniques. 
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Qualitative forecasting methodsGrass 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. 
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Quantitative forecasting methodsTime 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 nonlinear effects 
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How should we pick our forecasting modelData availability Time horizon for the forecast Required accuracy Required Resources 
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Time Series: Moving averageThe 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. 
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Time series: simple moving averageIn the simple moving average models the forecast value is At + At1 + … + Atn Ft+1 = n t is the current period. Ft+1 is the forecast for next period n is the forecasting horizon (how far back we look), A is the actual sales figure from each period. 
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Example: forecasting sales at KrogerKroger sells (among other stuff) bottled spring water What will the sales be for July? Month Bottles Jan 1,325 Feb 1,353 Mar 1,305 Apr 1,275 May 1,210 Jun 1,195 Jul ? 
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What if we use a 3month simple moving averageAJun + AMay + AApr FJul = = 1,227 3 What if we use a 5month simple moving average? AJun + AMay + AApr + AMar + AFeb FJul = = 1,268 5 
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5month average smoothes data more; 3month average more responsiveWhat do we observe? 5month MA forecast 3month MA forecast 
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Stability versus responsiveness in moving averages 
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Time series: weighted moving averageWe may want to give more importance to some of the data… Ft+1 = wt At + wt1 At1 + … + wtn Atn wt + wt1 + … + wtn = 1 t is the current period. Ft+1 is the forecast for next period n is the forecasting horizon (how far back we look), A is the actual sales figure from each period. w is the importance (weight) we give to each period 
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Why do we need the WMA modelsBecause of the ability to give more importance to what happened recently, without losing the impact of the past. 
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Example: Kroger sales of bottled waterWhat will be the sales for July? Month Bottles Jan 1,325 Feb 1,353 Mar 1,305 Apr 1,275 May 1,210 Jun 1,195 Jul ? 
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6month simple moving average…AJun + AMay + AApr + AMar + AFeb + AJan FJul = = 1,277 6 In other words, because we used equal weights, a slight downward trend that actually exists is not observed… 
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What if we use a weighted moving averageMake the weights for the last three months more than the first three months… The higher the importance we give to recent data, the more we pick up the declining trend in our forecast. 6month SMA WMA 40% / 60% WMA 30% / 70% WMA 20% / 80% July Forecast 1,277 1,267 1,257 1,247 
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How do we choose weightsDepending 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! 
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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. Denotes the importance of the past error Smoothing constant alpha ? 
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Why use exponential smoothingUses less storage space for data Extremely accurate Easy to understand Little calculation complexity There are simple accuracy tests 
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Exponential smoothing: the methodAssume that we are currently in period t. We calculated the forecast for the last period (Ft1) and we know the actual demand last period (At1) … The smoothing constant ? expresses how much our forecast will react to observed differences… If ? is low: there is little reaction to differences. If ? is high: there is a lot of reaction to differences. 
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Example: bottled water at KrogerMonth Actual Forecasted ? = 0.2 Jan 1,325 1,370 Feb 1,353 1,361 Mar 1,305 1,359 Apr 1,275 1,349 May 1,210 1,334 Jun ? 1,309 
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Example: bottled water at KrogerMonth Actual Forecasted ? = 0.8 Jan 1,325 1,370 Feb 1,353 1,334 Mar 1,305 1,349 Apr 1,275 1,314 May 1,210 1,283 Jun ? 1,225 
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Impact of the smoothing constant 
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TrendWhat do you think will happen to a moving average or exponential smoothing model when there is a trend in the data? 
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Impact of trendSales Regular exponential smoothing will always lag behind the trend. Can we include trend analysis in exponential smoothing? Month Actual Data Forecast 
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Exponential smoothing with trendFIT: Forecast including trend ?: Trend smoothing constant The idea is that the two effects are decoupled, (F is the forecast without trend and T is the trend component) 
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Example: bottled water at Kroger? = 0.8 At Ft Tt FITt ? = 0.5 Jan 1325 1380 10 1370 Feb 1353 1334 28 1306 Mar 1305 1344 9 1334 Apr 1275 1311 21 1290 May 1210 1278 27 1251 Jun 1218 43 1175 
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Exponential Smoothing with Trend 
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Linear regression in forecastingLinear regression is based on Fitting a straight line to data Explaining the change in one variable through changes in other variables. dependent variable = a + b ? (independent variable) By using linear regression, we are trying to explore which independent variables affect the dependent variable 
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Example: do people drink more when it’s coldAlcohol Sales Which line best fits the data? Average Monthly Temperature 
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The best line is the one that minimizes the errorThe predicted line is … So, the error is … Where: ? is the error y is the observed value Y is the predicted value 
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Least Squares Method of Linear RegressionThe goal of LSM is to minimize the sum of squared errors… 
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What does that meanAlcohol Sales So LSM tries to minimize the distance between the line and the points! Average Monthly Temperature 
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Least Squares Method of Linear RegressionThen the line is defined by 
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How can we compare across forecasting modelsWe need a metric that provides estimation of accuracy Forecast Error Errors can be: biased (consistent) random Forecast error = Difference between actual and forecasted value (also known as residual) 
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Measuring Accuracy: MFEMFE = Mean Forecast Error (Bias) It is the average error in the observations 1. A more positive or negative MFE implies worse performance; the forecast is biased. 
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Measuring Accuracy: MADMAD = Mean Absolute Deviation It is the average absolute error in the observations 1. Higher MAD implies worse performance. 2. If errors are normally distributed, then ??=1.25MAD 
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MFE & MAD: A Dartboard AnalogyLow MFE & MAD: The forecast errors are small & unbiased 
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An Analogy (cont’d)Low MFE but high MAD: On average, the arrows hit the bullseye (so much for averages!) 
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MFE & MAD: An AnalogyHigh MFE & MAD: The forecasts are inaccurate & biased 
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Key PointForecast 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 
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Measuring Accuracy: Tracking signalIf TS > 4 or < 4, investigate! 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 reevaluate using a model. 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 
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Example: bottled water at KrogerQuestion: Which one is better? Exponential Smoothing (? = 0.2) Forecasting with trend (? = 0.8) (? = 0.5) Month Actual Forecast Month Actual Forecast Jan 1,325 1370 Jan 1,325 1,370 Feb 1,353 1306 Feb 1,353 1,361 Mar 1,305 1334 Mar 1,305 1,359 Apr 1,275 1290 Apr 1,275 1,349 May 1,210 1251 May 1,210 1,334 Jun 1,195 1175 Jun 1,195 1,309 
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Bottled water at Kroger: compare MAD and TSWe observe that FIT performs a lot better than ES Conclusion: Probably there is trend in the data which Exponential smoothing cannot capture MAD TS Exponential Smoothing 70  6.0 Forecast Including Trend 33  2.0 
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Which Forecasting Method Should You UseGather 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 
«Forecasting» 