管理經(jīng)濟學-生意和經(jīng)濟的預測

1、Business and Economic ForecastingChapter 5 Demand Forecasting is a critical managerial activity which comes in two forms:Qualitative Forecasting Gives the Expected DirectionQuantitative ForecastingGives the precise Amount2.7654 %2002 South-Western Publishing 1Time-Series Characteristics: Secular Tre

2、nd and Cyclical Variation in Womens Clothing Sales2Time-Series Characteristics: Seasonal Pattern and Random Fluctuations3Microsoft Corp. Sales Revenue, 19842001Figure 6.24White Noise and MA(1) Time Series5A MA(1) Process A moving average process of order one MA(1) can be characterized as one where x

3、t = et + a1et-1, t = 1, 2, with et being an iid sequence with mean 0 and variance This is a stationary, weakly dependent sequence as variables 1 period apart are correlated, but 2 periods apart they are not6Three Stationary AR(1) Time Series7An AR(1) Process An autoregressive process of order one AR

4、(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 | 1 Corr(yt ,yt+h) = Cov(yt ,yt+h)/(y y) = 1h which becomes small as h increases8Three Stationary AR(1) Time Serie

5、s 9Stationary Stochastic Process A stochastic process is stationary if for every collection of time indices 1 t1 50%, improved conditions are expected50What Went Wrong With SUVs at Ford Motor Co?Chrysler introduced the Minivanin the 1980sFord expanded its capacity to produce the Explorer, its popula

6、r SUVExplorers price raised in 1995 substantiallyat same time as Chryslers Jeep Cherokeeand GM expanded its Chevrolet SUVMust consider response of rivals in pricing decisions51Quantitative ForecastingTime Series Looks For PatternsOrdered by TimeNo Underlying StructureEconometric ModelsExplains relat

7、ionshipsSupply & DemandRegression ModelsLike technicalsecurity analysisLike fundamentalsecurity analysis52Time SeriesExamine Patterns in the PastTIMEToXXXDependent Variable53Time Series is a quantitative forecasting methodUses past data to project the futurelooks for highest ACCURACY possibleAccurac

8、y (MSE & MAD) Mean Squared Error & Mean Absolute DeviationFt+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)| /N54Methods of Time Series Analysis for Economic Forecasting1. Naive ForecastFt+

9、1 = AtMethod best when there is no trend, only random errorGraphs of sales over time with and without trendsNO TrendTrend552. Moving AverageA smoothing forecast method for data that jumps aroundBest when there is no trend3-Period Moving Ave.Ft+1 = At + At-1 + At-2/3*ForecastLineTIMEDependent Variabl

10、e563. Exponential SmoothingA hybrid of the Naive and Moving Average methodsFt+1 = .At +(1-)Ft A weighted average of past actual and past forecast.Each forecast is a function of all past observationsCan show that forecast is based on geometrically declining weights.Ft+1 = .At +(1-)At-1 + (1-)2At-1 +

11、Find lowest MSE to pick the best alpha.574. Linear & 5. Semi-logUsed when trend has a constant AMOUNT of changeAt = a + bT, whereAt are the actual observations andT is a numerical time variableUsed when trend is a constant PERCENTAGE rateLog At = a + bT,where b is the continuously compounded growth

12、rateLinear Trend Regression Semi-log Regression58More on Semi-log Forma proofSuppose: Salest = Sales0( 1 + G) t where G is the annual growth rateTake 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 +

13、t gLn St = a + g t59Numerical 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 functionalform60The regression equation isS

14、ales = 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 0.00164

15、9 59.54 0.000s = 0.006899 R-sq = 99.9% R-sq(adj) = 99.9%61Forecasted Sales Time = 7Linear ModelSales = 85.0 + 12.7 TimeSales = 85.0 + 12.7 ( 7)Sales = 173.9Semi-Log ModelLn-sales = 4.50 + 0.0982 TimeLn-sales = 4.50 + 0.0982 ( 7 )Ln-sales = 5.1874To anti-log:e5.1874 = 179.0linear62Sales Time Ln-sales

16、100.0 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 isexponential7636. Procedures for Seasonal AdjustmentsTake ratios of A/F for past years. Find the average ratio. Adjust by this percentageIf a

17、verage ratio is 1.02, adjust forecast upward 2%Use 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.64Dummy Variables for Seasonal AdjustmentsLet D = 1, if 4th quarter and 0 otherwiseRun a

18、 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.EXAMPLE: 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) = 47865Dummy Variable InteractionsCan introduce a slope shifter by “interacting” two variablesA t = a + bT + cD + dDTc is the intercept shifterd is the slope shifterE.g., Sales = 300 + 10T + 18D - 3DTimplies that the Intercept is 318, when D = 1implies