【文章內(nèi)容簡(jiǎn)介】 is explained by national freight car loadings. 39 Ranging Forecasts ? Forecasts for future periods are only estimates and are subject to error. ? One way to deal with uncertainty is to develop bestestimate forecasts and the ranges within which the actual data are likely to fall. ? The ranges of a forecast are defined by the upper and lower limits of a confidence interval. 40 Ranging Forecasts ? The ranges or limits of a forecast are estimated by: Upper limit = Y + t(syx) Lower limit = Y t(syx) where: Y = bestestimate forecast t = number of standard deviations from the mean of the distribution to provide a given proba bility of exceeding the limits through chance syx = standard error of the forecast 41 Ranging Forecasts ? The standard error (deviation) of the forecast is puted as: 2yxy a y b x ys = n 2? ? ?42 Example: Railroad Products Co. ? Ranging Forecasts Recall that linear regression analysis provided a forecast of annual sales for RPC in year 8 equal to $ million. Set the limits (ranges) of the forecast so that there is only a 5 percent probability of exceeding the limits by chance. 43 Example: Railroad Products Co. ? Ranging Forecasts ? Step 1: Compute the standard error of the forecasts, syx. ? Step 2: Determine the appropriate value for t. n = 7, so degrees of freedom = n – 2 = 5. Area in upper tail = .05/2 = .025 Appendix B, Table 2 shows t = . 1 2 8 7 . 5 . 5 2 8 ( 9 3 ) . 0 8 0 1 ( 1 5 , 4 4 0 ) . 5 7 4 872yxs ?????44 Example: Railroad Products Co. ? Ranging Forecasts ? Step 3: Compute upper and lower limits. Upper limit = + (.5748) = + = Lower limit = (.5748) = = We are 95% confident the actual sales for year 8 will be between $ and $ million. 45 Seasonalized Time Series Regression Analysis ? Select a representative historical data set. ? Develop a seasonal index for each season. ? Use the seasonal indexes to deseasonalize the data. ? Perform lin. regr. analysis on the deseasonalized data. ? Use the regression equation to pute the forecasts. ? Use the seas. indexes to reapply the seasonal patterns to the forecasts. 46 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales. 47 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis ? Representative Historical Data Set Year Qtr. ($mil.) Year Qtr. ($mil.) 1 1 2 1 1 2 2 2 1 3 2 3 1 4 2 4 48 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis ? Compute the Seasonal Indexes Quarterly Sales Year Q1 Q2 Q3 Q4 Total 1 2 Totals Qtr. Avg. . .849 .751 .557 49 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis ? Deseasonalize the Data Quarterly Sales Year Q1 Q2 Q3 Q4 1 2 50 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis ? Perform Regression on Deseasonalized Data Yr. Qtr. x y x2 xy 1 1 1 1 1 2 2 4 1 3 3 9 1 4 4 16 2 1 5 25 2 2 6 36 2 3 7 49 2 4 8 64 Totals 36 204 51 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis ? Perform Regression on Deseasonalized Data Y = + 22 0 4 ( 7 4 . 0 1) 3 6 ( 3 4 1 . 3 9 )a 8 . 3 5 78 ( 2 0 4 ) ( 3 6 )????28 ( 3 4 1 . 3 9 ) 3 6 ( 7 4 . 0 1 )b 0 . 1 9 98 ( 2 0 4 ) ( 3 6 )????52 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis ? Compute the Deseasonalized Forecasts Y9 = + (9) = Y10 = + (10) = Y11 = + (11) = Y12 = + (12) = Note: Average sales are expected to increase by .199 million (about $200,000) per quarter. 53 Example: Computer Products Corp. ? Seasonalized Times Series Regression Analysis ? Seasonalize the Forecasts Seas. Deseas. Seas. Yr. Qtr. Index Forecast Forecast 3 1 .849 3 2 .751 3 3 .557 3 4 54 ShortRange Forecasts ? Time spans ranging from a few days to a few weeks ? Cycles, seasonality, and trend may have little effect ? Random fluctuation is main data ponent 55 Evaluating ForecastModel Performance Shortrange forecasting models are evaluated on the basis of three characteristics: ? Impulse response ? Noisedampening ability ? Accuracy 56 Evaluating ForecastModel Performance ? Impulse Response and NoiseDampening Ability ? If forecasts have little periodtoperiod fluctuation, they are said to be noise dampening. ? Forecasts that respond quickly to changes in data are said to have a high impulse response. ? A forecast system that responds quickly to data changes necessarily picks up a great deal of random fluctuation (noise). ? Hence, there is a tradeoff between high impulse response and