管理经济学--生意和经济的预测68课件

Time-Series Characteristics:Secular Trend and Cyclical Variation in Womens Clothing SalesTime-Series Characteristics:Seasonal Pattern and Random FluctuationsMicrosoft Corp.Sales Revenue,19842001Figure 6.2Figure 6.2White Noise and MA(1)Time SeriesA MA(1)Processv A moving average process of order one MA(1)can be characterized as one where xt=et+a1et-1,t=1,2,with et being an iid sequence with mean 0 and variance v This is a stationary,weakly dependent sequence as variables 1 period apart are correlated,but 2 periods apart they are notThree Stationary AR(1)Time SeriesAn AR(1)Processv An autoregressive process of order one AR(1)can be characterized as one where yt=yt-1+et,t=1,2,with et being an iid sequence with mean 0 and variance2 For this process to be weakly dependent,it must be the case that|1v Corr(yt,yt+h)=Cov(yt,yt+h)/(y y)=1h which becomes small as h increasesThree Stationary AR(1)Time Series Stationary Stochastic Processv A stochastic process is stationary if for every collection of time indices 1 t1 50%,improved conditions are expectedWhat Went Wrong With SUVs at Ford Motor Co?vChrysler introduced the Minivanin the 1980svFord expanded its capacity to produce the Explorer,its popular SUVvExplorers price raised in 1995 substantiallyat same time as Chryslers Jeep Cherokeeand GM expanded its Chevrolet SUVvMust consider response of rivals in pricing decisionsQuantitative ForecastingvTime Series Looks For PatternsOrdered by TimeNo Underlying StructurevEconometric ModelsExplains relationshipsSupply&DemandRegression ModelsLike technicalsecurity analysisLike fundamentalsecurity analysisTime SeriesExamine Patterns in the PastTIME ToXXXDependent VariablevTime Series is a quantitative forecasting methodUses past data to project the futurelooks for highest ACCURACY possiblevAccuracy(MSE&MAD)Mean Squared Error&Mean Absolute DeviationvFt+1=f(At,At-1,At-2,.)Let F=forecast and Let A=actual data MSE=t=1 Ft-At 2/NThe LOWER the MSE or MAD,the greater the accuracyMAD=t=1|(Ft-At)|/NMethods of Time Series Analysis for Economic Forecasting1.Naive ForecastFt+1=AtMethod best when there is no trend,only random errorGraphs of sales over time with and without trendsNO TrendTrend2.Moving AveragevA smoothing forecast method for data that jumps aroundvBest when there is no trendv3-Period Moving Ave.Ft+1=At+At-1+At-2/3*ForecastLineTIMEDependent Variable3.Exponential SmoothingvA hybrid of the Naive and Moving Average methodsvFt+1=.At+(1-)Ft vA weighted average of past actual and past forecast.vEach forecast is a function of all past observationsvCan show that forecast is based on geometrically declining weights.Ft+1=.At+(1-)At-1+(1-)2 At-1 +Find lowest MSE to pick the best alpha.4.Linear&5.Semi-loglUsed when trend has a constant AMOUNT of changeAt=a+bT,whereA At t are the actual observations andT T is a numerical time variablelUsed when trend is a constant PERCENTAGE rateLog At=a+bT,where b b is the continuously compounded growth rateLinear Trend Regression Semi-log RegressionMore on Semi-log Forma proofvSuppose:Salest=Sales0(1+G)t where G is the annual growth ratevTake the natural log of both sides:Ln St=Ln S0+t Ln(1+G)but Ln(1+G)=g,the equivalent continuously compounded growth rateSO:Ln St=Ln S0+t gLn St=a +g tNumerical Examples:6 observationsMTB Print c1-c3.Sales Time Ln-sales100.0 1 4.60517109.8 2 4.69866121.6 3 4.80074133.7 4 4.89560146.2 5 4.98498164.3 6 5.10169Using this salesdata,estimate sales in period 7using a linear and a semi-log functionalformThe regression equation isSales=85.0+12.7 TimePredictor Coef Stdev t-ratio pConstant 84.987 2.417 35.16 0.000Time 12.6514 0.6207 20.38 0.000s=2.596 R-sq=99.0%R-sq(adj)=98.8%The regression equation isLn-sales=4.50+0.0982 TimePredictor Coef Stdev t-ratio pConstant 4.50416 0.00642 701.35 0.000Time 0.098183 0.001649 59.54 0.000s=0.006899 R-sq=99.9%R-sq(adj)=99.9%Forecasted Sales Time=7vLinear ModelvSales=85.0+12.7 TimevSales=85.0+12.7(7)vSales=173.9vSemi-Log ModelvLn-sales=4.50+0.0982 TimevLn-sales=4.50+0.0982(7)vLn-sales=5.1874vTo anti-log:e5.1874=179.0linearSales Time Ln-sales100.0 1 4.60517109.8 2 4.69866121.6 3 4.80074133.7 4 4.89560146.2 5 4.98498164.3 6 5.10169179.07 semi-log173.97 linearWhich prediction do you prefer?Semi-log isexponential76.Procedures for Seasonal AdjustmentsvTake ratios of A/F for past years.Find the average ratio.Adjust by this percentageIf average ratio is 1.02,adjust forecast upward 2%vUse Dummy Variables in a regression:D=1 if 4th quarter;0 otherwise12-quarters of dataI II III IV I II III IV I II III IVQuarters designated with roman numerals.Dummy Variables for Seasonal AdjustmentsvLet D=1,if 4th quarter and 0 otherwisevRun a new regression:A t=a+bT+cD the“c”coefficient gives the amount of the adjustment for the fourth quarter.It is an Intercept Shifter.vEXAMPLE:Sales=300+10T+18D12 Observations,1999-I to 2001-IV,Forecast all of 2002.Sales(2002-I)=430;Sales(2002-II)=440;Sales(2002-III)=450;Sales(2002-IV)=478Dummy Variable InteractionsvCan introduce a slope s