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1ForecastingSession 3Course: Quantitative MethodsYear: 20132Outline TodaysForecasting ApproachesOverview of Qualitative MethodsOverview of Quantitative MethodsTime-Series ForecastingDecomposition of a Time SeriesNaive ApproachMoving AveragesExponential SmoothingExponential Smoothing with Trend AdjustmentTrend ProjectionsSeasonal Variations in DataCyclical Variations in Data

3What is Forecasting?Process of predicting a future eventUnderlying basis of all business decisionsProductionInventoryPersonnelFacilities??4Seven Steps in ForecastingDetermine the use of the forecastSelect the items to be forecastedDetermine the time horizon of the forecastSelect the forecasting model(s)Gather the dataMake the forecastValidate and implement results5TrendSeasonalCyclicalRandomTime Series Components6Components of DemandDemand for product or service||||1234YearAverage demand over four yearsSeasonal peaksTrend componentActual demandRandom variation7Persistent, overall upward or downward patternChanges due to population, technology, age, culture, etc.Typically several years duration Trend Component8Regular pattern of up and down fluctuationsDue to weather, customs, etc.Occurs within a single year Seasonal ComponentNumber ofPeriodLengthSeasonsWeekDay7MonthWeek4-4.5MonthDay28-31YearQuarter4YearMonth12YearWeek529Repeating up and down movementsAffected by business cycle, political, and economic factorsMultiple years durationOften causal or associative relationshipsCyclical Component0510152010Erratic, unsystematic, residual fluctuationsDue to random variation or unforeseen eventsShort duration and nonrepeating Random ComponentMTWTF11Naive ApproachAssumes demand in next period is the same as demand in most recent periode.g., If January sales were 68, then February sales will be 68Sometimes cost effective and efficientCan be good starting point

12MA is a series of arithmetic means Used if little or no trendUsed often for smoothingProvides overall impression of data over timeMoving Average MethodMoving average = demand in previous n periodsn13January10February12March13April16May19June23July26Actual3-MonthMonthShed SalesMoving Average(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3Moving Average Example101213(10 + 12 + 13)/3 = 11 2/3Graph of Moving Average||||||||||||JFMAMJJASONDShed Sales30 28 26 24 22 20 18 16 14 12 10 Actual SalesMoving Average Forecast15Used when trend is present Older data usually less importantWeights based on experience and intuitionWeighted Moving AverageWeightedmoving average= (weight for period n) x (demand in period n) weights16January10February12March13April16May19June23July26Actual3-Month WeightedMonthShed SalesMoving Average[(3 x 16) + (2 x 13) + (12)]/6 = 141/3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2Weighted Moving Average101213[(3 x 13) + (2 x 12) + (10)]/6 = 121/6Weights AppliedPeriod3Last month2Two months ago1Three months ago6Sum of weightsIncreasing n smooths the forecast but makes it less sensitive to changesDo not forecast trends wellRequire extensive historical dataPotential Problems With Moving Average18Moving Average And Weighted Moving Average30 25 20 15 10 5 Sales demand||||||||||||JFMAMJJASONDActual salesMoving averageWeighted moving average19Form of weighted moving averageWeights decline exponentiallyMost recent data weighted mostRequires smoothing constant ()Ranges from 0 to 1Subjectively chosenInvolves little record keeping of past dataExponential Smoothing20Exponential SmoothingNew forecast =Last periods forecast+ a (Last periods actual demand Last periods forecast)Ft = Ft 1 + a(At 1 - Ft 1)whereFt=new forecastFt 1=previous forecasta=smoothing (or weighting) constant (0 a 1)21Exponential Smoothing ExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .2022Exponential Smoothing ExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20New forecast= 142 + .2(153 142)23Exponential Smoothing ExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant a = .20New forecast= 142 + .2(153 142)= 142 + 2.2= 144.2 144 cars24Common Measures of ErrorMean Absolute Deviation (MAD)MAD = |Actual - Forecast|nMean Squared Error (MSE)MSE = (Forecast Errors)2nCommon Measures of ErrorMean Absolute Percent Error (MAPE)MAPE =100|Actuali - Forecasti|/Actualinni = 1Exponential Smoothing with Trend AdjustmentWhen a trend is present, exponential smoothing must be modifiedForecast including (FITt) = trendExponentiallyExponentiallysmoothed (Ft) +(Tt)smoothedforecasttrend27Exponential Smoothing with Trend AdjustmentFt = a(At - 1) + (1 - a)(Ft - 1 + Tt - 1)Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1Step 1: Compute FtStep 2: Compute TtStep 3: Calculate the forecast FITt = Ft + Tt28Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.002173204195246217318289361029Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021732041952462173182893610Table 4.1F2 = aA1 + (1 - a)(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)= 2.4 + 10.4 = 12.8 unitsStep 1: Forecast for Month 230Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.8032041952462173182893610T2 = b(F2 - F1) + (1 - b)T1T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 unitsStep 2: Trend for Month 231Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.801.9232041952462173182893610FIT2 = F2 + T1FIT2 = 12.8 + 1.92= 14.72 unitsStep 3: Calculate FIT for Month 232Exponential Smoothing with Trend Adjustment ExampleForecastActualSmoothedSmoothedIncludingMonth(t)Demand (At)Forecast, FtTrend, TtTrend, FITt11211213.0021712.801.9214.723204195246217318289361015.182.1017.2817.822.3220.1419.912.2322.1422.512.3824.8924.112.0726.1827.142.4529.5929.282.3231.6032.482.6835.1633Exponential Smoothing with Trend Adjustment Example|||||||||123456789Time (month)Product demand35 30 25 20 15 10 5 0 Actual demand (At)Forecast including trend (FITt)with = .2 and = .434Trend ProjectionsFitting a trend line to historical data points to project into the medium to long-rangeLinear trends can be found using the least squares techniquey = a + bx^where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable^35Least Squares MethodTime periodValues of Dependent VariableDeviation1(error)Deviation5Deviation7Deviation2Deviation6Deviation4Deviation3Actual observation (y value)Trend line, y = a + bx^36Least Squares MethodTime periodValues of Dependent VariableDeviation1Deviation5Deviation7Deviation2Deviation6Deviation4Deviation3Actual observation (y value)Trend line, y = a + bx^Least squares method minimizes the sum of the squared errors (deviations)37Least Squares MethodEquations to calculate the regression variablesb =Sxy - nxySx2 - nx2y = a + bx^a = y - bx38Least Squares Exampleb = = = 10.54xy - nxyx2 - nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70TimeElectrical Power YearPeriod (x)Demandx2xy20011741742002279415820033809240200449016360200551052552520056142368522007712249854x = 28y = 692x2 = 140xy = 3,063x = 4y = 98.8639Least Squares Exampleb = = = 10.54Sxy - nxySx2 - nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70TimeElectrical Power YearPeriod (x)Demandx2xy19991741742000279415820013809240200249016360200351052552520046142368522005712249854Sx = 28Sy = 692Sx2 = 140Sxy = 3,063x = 4y = 98.86The trend line isy = 56.70 + 10.54x^40Least Squares Example|||||||||200120022003200420052006200720082009160 150 140 130 120 110 100 90 80 70 60 50 YearPower demandTrend line,y = 56.70 + 10.54x^41Least Squares RequirementsWe always plot the data to insure a linear relationshipWe do not predict time periods far beyond the databaseDeviations around the least squares line are assumed to be random42ReferenceDavid R. Anderson [et.al]. (2008). Quantitative Methods for Business. 11. SOWES. New York. ISBN: 10: 0324651813.Bina Nusantara University43Bina Nusantara University44Thank You