二次曲线指数平滑法课件.pptx

1、一次移动平均法一次指数平滑法线性二次移动平均法线性二次指数平滑法二次曲线指数平滑法一次移动平均法一次移动平均法一次指数平滑法一次指数平滑法010203040506070051015销售额预测值91929394959697989910005101520销售额预测值有明显的线性变化趋势时用线性二次移动平均法 线性二次指数平滑法0501001502002503000246810121416销售额销售额销售额应用背景：有的时间序列虽然有增加或减少趋势，但不一定是线性的，可能按二次曲线的形状增加而减少。01020304050601980198519901995200020052010销售额年度 对于这种

2、非线性增长的时间序列，采用二次曲线指数平滑法可能要比线性指数平滑法更为有效。它的特点是不但考虑了线性增长的因素，而且也考虑了二次抛物线的增长因素。二次曲线指数平滑法的计算过程共分七个步骤。1.计算t时期的单指数平滑值2.计算t时期的双指数平滑值3.计算t时期的三重指数平滑值 1tS 1111tttSxS 2tS 21211tttSSS 3tS 32311tttSSS4.计算t时期的水平值5.计算t时期的线性增量6.计算t时期 的抛物线增量tA 12333ttttASSStB 212326 510 84 31ttttBSSStC 2123221ttttCSSS7.预测m时期以后，即 时期的数值虽

3、然二次曲线指数平滑法的计算方法比前几种指数平滑法复杂，但对非平稳时间序列的预测相当有效，它能随着时间序列呈抛物线增长而调整预测值。()t mt mF212t mtttFABmC m 修正的 修正的 修正的t 3312ttttSSSS 2223ttttSSSS 1112ttttSSSS 112333tttttSASSStB 212326 510 84 31ttttBSSS 122312235131ttttttttSSSSSSSS某地区统计了从19832006年每年的消费品销售总额，数据如下表，通过计算机求解平滑常数最佳值为0.5，此时对应均方差最小，逐年预测，m=1，计算结果如下。 1110.5

4、0.5tttSxS 21210.50.5tttSSS 32310.50.5tttSSS 12333ttttASSS 1233.562.5ttttBSSS 1232ttttCSSS212tmtttFAB mC mt年度观测值（x）1198312.912.912.912.92198414.9113.90513.402513.1512514.658751.1306250.251253198515.9614.932514.167513.6593815.954381.4071880.25687515.9154198614.4114.6712514.4193814.0393814.795-0.06844-

5、0.1281317.495198714.5714.6206314.5214.2796914.58156-0.24859-0.1396914.66256198814.614.6103114.5651614.4224214.55789-0.19879-0.0975814.263137198915.3514.9801614.7726614.5975415.220040.2884570.03238314.310318199015.8415.4100815.0913714.8444515.800590.4982030.07179715.524699199116.916.1550415.623215.23

6、38316.829340.8879880.14246116.3346910199218.2617.2075216.4153615.8245918.201071.2956370.20139217.7885511199317.417.3037616.8595616.3420817.674680.26099-0.0732819.597412199418.7118.0068817.4332216.8876518.608630.6438810.02808817.8990213199519.5318.7684418.1008317.4942419.497070.8201580.06101919.26655

7、14199620.8219.7942218.9475318.2208820.760971.1468250.12005220.3477415199722.8721.3321120.1398219.1803522.757231.7743550.23282521.9678216199824.5922.9610521.5504420.3653924.597251.9745580.22557624.6479917199925.9324.4455322.9979821.6816926.024321.7756740.13125126.6845918200028.0426.2427624.6203723.15

8、10328.01822.0050120.15304827.8656219200129.4527.8463826.2333824.692229.531221.7925820.07183130.0997420200231.4729.6581927.9457826.3189931.456211.9264480.08561731.3597121200333.9931.824129.8849428.1019733.919432.3296120.15618333.4254722200439.5635.6920532.7884930.4452339.155894.304280.56029136.327142

9、3200548.0841.8860237.3372633.8912447.537547.3056421.10275143.7403224200653.6747.7780142.5576438.2244453.885577.4383290.88718155.3945625200761.76749 1tS 2tS 3tStAtBtCt mF01020304050601980198519901995200020052010观测值S1051015202530354045501980198519901995200020052010S1S20510152025303540451980198519901995200020052010S2S30102030405060701980198519901995200020052010S3F0102030405060701980198519901995200020052010观测值F0102030405060701980198519901995200020052010观测值S1S2S3F