《预测与决策技术应用》时间序列分析报告地报告材料：美国AcmeTool公司1994-2000年销售额记录簿

实用标准文案实用标准文案精彩文案精彩文案美国AcmeTool公司1994-2000年销售额记录

T= 10.3年份 季

时期 销售 S1(α S2(α/t额/X=0.3)=0.3)/t额/X=0.3)=0.3)=0.3误差方1433.3433.3433.30.0

Y/α

误差平23200.0200.03200.0200.0200.00.04366.7366.7366.70.011500453.3439.3467.36.0433.366.74444.422350315.0304.5325.54.5300.050.02500.033250215.0204.5225.54.5200.050.02500.044400376.7369.7383.73.0366.733.31111.115450452.3443.2461.43.9473.323.3544.426350325.5310.8340.26.3330.020.0400.037200210.5206.3214.71.8230.030.0900.048300353.7364.9342.5-4.8386.786.77511.119350421.6436.8406.5-6.5465.3115.313301.8210200287.9303.9271.8-6.9346.5146.521462.3311150192.4202.1182.6-4.2216.566.54422.3412400367.6365.7369.50.8337.762.33885.4113550460.1443.8476.57.0400.0150.022490.0214350306.5304.7308.30.8264.985.17242.0315250209.6204.4214.92.3178.471.65126.6416550422.3382.7461.917.0370.3179.732304.1117550487.1456.8517.413.0483.566.54417.8218400334.5313.6355.49.0309.190.98267.4319350251.8218.6284.914.2217.2132.817642.5420600475.6410.5540.727.9478.9121.114661.2121750566.0489.5642.432.8530.4219.648210.8222500384.2334.8433.621.2364.4.618386.3323400296.2241.9350.623.3299.1100.910175.0

300.0 300.0 300.0 0.0-19941995199619971998199920002000424650527.9445.8610.135.2568.681.46633.7125850651.2538.0764.348.5675.2174.830565.1226600448.9369.0528.834.2454.7145.321106.6327450342.4272.0412.730.1373.976.15796.6428700579.5485.9673.240.1645.354.72991.6129812.82001230预测563.0均方差331442.8432713.3平均-94.211392.9误差700700600500ESQ400300200051015202530SQ趋势图趋势图900销售额/XY/α=0.3额500金1001591317212529图1-1：原《美国AcmeTool公司1994-2000年销售额记录表》数据图。图1-2：原《美国AcmeTool公司1994-2000年销售额记录表》数据图与“α＝0.3”的二次指数平滑法预测数据趋势图。【预测】.200112的时候，得到预测值分别是：20011924.220012649.2美国AcmeTool公司1994-2000年销售额记录

T= 10.5年份年份季度/t销售额/XS1(α=0.5)S2(α=0.5)abY(α=0.5)绝对误差误差平方1433.3433.3433.3300.0200.0.0-0--2300.0300.00.03200.0200.00.004366.7366.74366.7366.711500466.7450.022350325.0312.5199433250225.0212.544400383.3375.015450458.3454.226350337.5325.0199537200212.5212.548300341.7358.319350404.2429.2210200268.8296.91996311150181.3.9412400370.8364.6113550477.1453.11997214350309.4303.1315250215.6206.30.016.7433.366.74444.412.5300.050.02500.012.5200.050.02500.08.3366.733.31111.14.2500.050.02500.012.5350.00.00.00.0250.050.02500.0-16.7400.0100.010000.0-25.0466.7116.713611.1-28.1362.5162.526406.3-15.6212.562.53906.36.3308.391.78402.824.0354.2.838350.76.3212.5137.518906.39.4150.0100.010000.07483.3337.5237.5391.7462.5350.0212.5325.0379.2240.6165.6377.1501.0315.6225.0416550416550460.4412.5117550513.5483.31998218400354.7328.9319350282.8244.5420600530.2471.4121750631.8557.61999222500427.3378.1323400341.4293.0424650590.1530.7125850740.9649.22000226600513.7445.9327450395.7344.3428700645.1587.912947.9383.3166.727777.830.2525.025.0625.025.8321.978.16103.538.3234.4115.613369.158.9556.343.81914.174.2574.0176.030990.749.2406.393.88789.148.4359.440.61650.459.4647.92.14.391.7780.269.84870.967.8525.874.25508.451.4438.311.7137.357.2708.98.978.4924.23543.8380.5321.1589.1706.0476.6389.8649.5832.6581.4447.1702.22 3020013 314 32平均

649.2预测498.4759.4-

均方差77.6 8819.9700700600500ESQ400300200051015202530SQ误差趋势图趋势图1000销售额/XY(α=0.5)700额金4001001357911 13151719 21 2325 2729 31图1-1：原《美国AcmeTool公司1994-2000年销售额记录表》数据图。图1-3：原《美国AcmeTool公司1994-2000年销售额记录表》数据图与“α＝0.5”的二次指数平滑法预测数据趋势图。【预测】.200112的时候，得到预测值分别是：20011924.220012649.2美国AcmeTool公司1994-2000年销售额记录

T= 1年份季度时期销售S1(α年份季度时期销售S1(αS2(αab绝对误差平-2340-300.0200.0366.7300.0200.0366.7300.0200.0366.70.00.00.0-/t额/X=0.7)=0.7)=0.7)误差方1433.3433.3433.30.011500480.0466.0494.032.7433.366.74444.419922350335.0324.5345.524.5300.050.02500.0433250235.0224.5245.524.5200.050.02500.044400390.0383.0397.016.3366.733.31111.115450459.0461.1456.9-4.9526.776.75877.819926350345.5339.2351.814.7370.020.0400.0537200210.5214.7206.3-9.8270.070.04900.048300327.0343.8310.2-39.2413.3113.312844.419350382.7406.2359.2-54.9452.0102.010404.0199210200243.7272.3215.0-66.9366.5166.527722.36311150168.2182.1154.2-32.6.546.52162.3412400378.1367.8388.424.0271.0129.016641.0113550499.8471.7527.965.5304.3245.760368.5199214350318.1304.4331.832.0148.1201.940763.67315250225.4212.4238.430.3121.6128.416486.6416550498.4459.2537.691.4412.4137.618933.8117550534.9516.0553.944.2593.443.41883.6199218400375.4354.1396.749.7363.936.11305.08319350312.6282.6342.770.1268.881.26597.5420600569.5536.4602.677.2629.129.1843.9121750685.5634.6736.3118.7598.2151.823057.5199222500462.6430.1495.276.0446.553.52862.79323400373.8346.4401.263.8412.812.8164.4424650625.9599.0652.762.6679.829.8888.9125850800.6750.8850.4116.2855.05.024.9200226600558.8520.2597.490.1571.128.9832.40327450427.1402.9451.456.5465.015.0225.1428700677.8654.1701.455.1715.315.3233.3200122930966.7687.51331预测 均方差507.8432756.5700700600500ESQ400300200051015202530SQ平均误差-76.49535.0135791113151719212325272931时期1-1AcmeTool公司1994-2000年销售额记录表》数据图。图1-4：原《美国AcmeTool公司1994-2000趋势图1000趋势图1000销售额/XY(α=0.7)700额金400100【预测】.200112的时候，得到预测值分别是：20011966.720012687.5年份第一季度第二季度第三季度第四季度2003490267643984032004667307649844902（单位万元年份第一季度第二季度第三季度第四季度2003490267643984032004667307649844902005200575031685551861【解】.0202468101214JD5,0004,000R 3,000S2,0001,0000图2-1：原《某旅游风景区2003-2005年的旅游收入资料》数据图。t)t)3份45季节指数4.000合计季平均第一季度第二季度第三季度第四季度2004902676439840379671991.75年2006673076498449092172304.2520075031685551861103302582.50季合计 19078920149331754同季平均 635.672973.334977.67584.67275142292.830.277241.296792.170970.25500修正指数27.72%129.68217.1025.50%400.00%%%%2006预测8303882.336499.42763.4160006000序列数t趋势数T4000额售销20000123456789101112季度2-22003-2005指数预测法的预测数据趋势图。【题3】.利用时间序列分解法预测1996年第一、二月份的社会消费品零售总额。【解】.T(Trendcomponent)、季节变动S(Seasonalcomponent)C(CyclicalI(Irregular时间序列分解法的乘法模式：Xt

TSCt t

I（其中，Xt

与T有相同的量纲；t tSt

I是独立随机变量序列，服从正t t态分布。）因素(T(S(C(T(S其中，通过移动平均数——消除了季节因素和随机因素，可求出趋势－循环因子。即利用MA(N)TCSIt t t t t

TCT与循环变t t动因素C 的乘机序列数：Tt

Ct1980-1995年各月社会消费品零售总额（亿元）日期零售额TC序号均方误差1980-1995年各月社会消费品零售总额（亿元）日期零售额TC序号均方误差1980M011980M021980M031980M041980M051980M061980M071980M081980M091980MMt(12)190.3269.9118054.1174.9269.9126780.2.2269.9135664.4168.4269.9244761.6168.6269.9254058.2168.2269.9263566.6.5173.4994.24%269.920.6473388.0161.6174.5392.59%269.920.6583481.6172.9175.4798.53%269.920.6593827.2166.5176.9594.09%269.930.66104542.1101980M111980M

175.2

178.25 98.29% 269.930.66 110.15

5821.8121981M011981M021981M031981M041981M051981M061981M071981M081981M091981M101981M111981M

.7 172.58 %177.9174.65%177.9174.65181.5298.01%269.960.6714182.9 176.29 %184178.89%184178.89185.3099.30%270.010.6917182.4180.08187.2597.41%270.040.6918175.6181.08.2892.77%270.070.7019172181.95190.3590.36%270.100.7020184.9182.95191.5096.55%270.140.7121184.7184.47193.2495.58%270.190.7222.1 .13 .73

%117.46100.25%100.27100.19%114.51

269.940.66 12269.950.67 13269.970.68 15269.990.68 16121982M011982M

224.8 233.6 182

.31.87.18

%118.06270.240.72270.240.7223270.300.7324270.370.732591.38% 270.450.74 26021982M031982M041982M051982M061982M071982M081982M091982M101982M111982M121983M011983M021983M031983M04221213.71221213.71222.3399.40%273.220.8141051983M220.5215.20224.9698.02%273.560.8242

206.6 192.49 248.2 204.93 243.2 205.73 217.5 208.69 226.2 210.33 223.5 212.10

103.11202.2193.99202.2193.99201.53270.630.7428%201.7.47202.5499.59%270.740.7529202.6.15203.9699.33%270.860.7530192.8.58205.3393.90%271.000.7631.2.77207.2189.86%271.140.7632.3200.97209.5195.13%271.300.7733.2202.09211.2193.84%271.480.7834205.8202.98212.9096.66%271.670.7835115.74%112.73%100.16%103.37%101.42%

270.540.74 27271.880.7936272.110.7937272.350.8038272.620.8039272.910.8140061983M071983M081983M091983M101983M111983M121984M011984M021984M031984M041984M051984M061984M071984M081984M091984M

235282

223.55 226.37

205.8216.28205.8216.28227.4290.49%273.910.8343206.9218.01228.8990.39%274.300.8344218.8219.63230.2495.03%274.710.8445216221.12232.1593.04%275.150.8446%119.04268.4228.47268.4228.47239.91111.87%276.660.8749227.6229.31243.3593.53%277.230.8850248.6231.18247.35100.50%277.830.8951247233.13252.2097.94%278.470.9152249.9235.54257.4997.05%279.150.9253253.1238.26263.6995.98%279.860.9454245.5241.57270.1490.88%280.620.9655249.6245.13276.9590.12%281.420.9856272.3249.58283.3296.11%282.271.0057278.7254.81287.6196.90%283.161.0258

275.620.85 47276.130.86 48101984M111984M121985M011985M021985M031985M041985M051985M061985M071985M081985M091985M101985M111985M121986M01

299.4 260.18 366.3 267.20 338.9 273.08 320.6 280.83 308.5 285.82 341.7 313.05 411.1 316.78 381.6 320.34

102.83%124.32%113.75%106.55%%290.1%290.1289.41307.8394.24%289.541.0664291.8292.90311.2993.74%290.801.0765295.2296.41314.9293.74%292.121.0866282299.45318.5688.52%293.491.0967284.2302.33321.4088.43%294.931.0968317.8306.13323.5898.22%296.441.0969319.5309.53326.3397.91%298.011.1070103.65%123.35%113.23%

284.091.0259285.081.0360286.111.0461287.201.0562288.351.06 63299.651.1071301.361.1172303.141.11731986M

346

322.46 340.93

305.001.12 74021986M031986M041986M051986M061986M071986M081986M091986M101986M111986M121987M011987M021987M031987M041987M051987M

378.3 348.04 382 353.25 405.4 358.56 481.2 364.40

%335.3%335.3324.69345.5297.04%306.931.1375329.4327.97350.6593.94%308.951.1376332.9331.39355.9093.54%311.041.1477340.2335.14361.4894.11%313.221.1578326.6338.86367.0588.98%315.491.1679333.9343.00371.7089.83%317.841.1780320.281.17320.281.1781322.811.1882325.441.1883328.171.1984%105.22%123.33445.2369.70445.2369.70395.38112.60330.991.1985394.1373.71400.64%98.37%333.911.2086391.5378.39405.7896.48%336.941.2087383.9382.93411.1993.36%340.081.2188389.7387.67416.8193.50%343.321.2189400.7392.71422.9094.75%346.681.2290061987M071987M081987M091987M101987M111987M121988M011988M021988M031988M041988M051988M061988M071988M081988M

390.7 398.05 429.71 90.92% 350.151.23 91396.1 403.23 438.53 90.33% 353.731.24 92439.3 408.32 447.90 98.08% 357.441.25 93451 414.07 455.96 98.91% 361.261.26 94365.211.27365.211.2795369.291.2896373.491.2997471.2 419.55 464.15%118.65561.6 426.25 473.31%109.25528.2 433.17 483.50%522.7443.88522.7443.88495.43377.831.3198%487.9451.92508.9295.87%382.301.3399481460.01521.0892.31%386.911.35100489.1468.29531.2792.06%391.671.36101521.2478.33540.3096.47%396.561.36102514.7488.67549.1593.73%401.601.37103558.4502.19100.14557.61 406.791.37 104%106.04600.8 515.65 566.5509

412.131.37 1051988M

581.2 526.50 575.80

417.621.38 106101988M111988M121989M011989M021989M031989M041989M051989M061989M071989M081989M091989M101989M111989M121990M

585.7 536.04 663.7 544.55 638.5 553.74 615.6 561.48 01%1990M01%1990M574.6588.26584.6398.28%529.111.10122

%100.36%112.66%107.80%103.79609.6571.63609.6571.63592.01102.97447.531.32111%581.1579.97591.0398.32%454.021.30112575.6587.18590.4197.49%460.681.28113567.2591.01590.2796.09%467.521.26114546.2593.63591.0292.42%474.551.25115546.1592.61589.9792.56%481.761.22116586.5591.42586.8199.95%489.161.20117571.8590.63584.4797.83%496.751.18118580.3590.18583.3999.47%504.541.16119665.8590.36114.13583.36 512.531.14 120%112.08

423.281.38107429.091.37108435.071.36109441.211.34110520.711.12 121021990M031990M041990M051990M061990M071990M081990M091990M101990M111990M121991M011991M021991M031991M041991M051991M

640.6 595.87 735.3 601.66 709.7 606.28

574.8585.36574.8585.36586.1998.06%537.711.09123559.8583.58589.0095.04%546.531.08124570.9583.19593.3596.22%555.561.07125571.3583.53598.7695.41%564.811.06552.2584.03603.9791.43%574.281.05127560.4585.23611.7191.61%583.981.05128609.6587.15620.0598.32%593.911.04129616.1590.84626.7398.30%604.081.04130614.481.03614.481.03131625.121.02132636.011.01%110.01%705.1617.15705.1617.15651.22647.141.01134644.3622.94657.86%97.94%658.531.00650.7630.52665.1897.82%670.170.99136635.9635.93672.9394.50%682.080.99137645.7642.13680.9194.83%694.240.98061991M071991M081991M091991M101991M111991M121992M011992M021992M031992M041992M051992M061992M071992M081992M091992M

736 676.90 831.6 684.93 811.3 693.39 811.4 702.25

624.2648.13624.2648.13689.1690.57%706.680.98634.5654.31697.8290.93%719.380.97140694.8661.41707.5998.19%732.360.97141706.6668.95715.7798.72%745.620.96142759.160.95759.160.95143772.990.95144787.110.94145801.530.93146%109.78%108.50772.4712.93772.4712.93757.38101.98816.240.93147719718.62767.83%93.64%831.260.92148729726.38778.7793.61%846.590.92149745.4734.68792.5194.06%862.230.92150728.7743.39807.6490.23%878.180.92151741.6752.32817.9590.67%894.450.91152816.2762.43828.4098.53%911.050.91153836.2773.23844.7598.99%927.980.91154101992M111992M121993M011993M021993M031993M041993M051993M061993M071993M081993M091993M101993M111993M121994M011994M

945.240.91 155868.8784.30863.73100.59868.8784.30863.73100.59%1028.116.326800.72884.29%977.5814.57904.93108.02%892.5821.33923.8296.61%942.3835.48941.54100.08%941.3854.01959.1298.14%962.2873.44977.7998.41%1005.1003.6100.217895.133%963.8914.731028.793.69%01048.9959.8932.91091.51%1023.950.171069.495.68%381051.1088.61968.08196.55%1102987.511108.999.38%01415.1019.71129.0125.37558%1192.1037.61150.7103.60248%1162.1060.11176.398.84%980.780.92 157999.060.92 1580.931590.931590.931600.931610.931620.940.941640.941650.941660.941670.941680.941690.9417001036.691056.041075.751095.831116.291137.121158.331179.941201.931224.321247.1021994M031994M041994M051994M061994M071994M081994M091994M101994M111994M121995M011995M021995M031995M041995M05

71166.11176.61213.71238.71251.5128613991444.11553.81992.31602.21491.51533.31548.71585.4

96.72%95.07%95.35%94.15%92.24%92.68%98.76%99.77%105.10%131.89%103.85%94.82%95.69%94.84%95.26%

10.951710.951710.961720.971730.981740.991751.001761.001771.001781.001791.011801.011811.011821.011831.011841.011851.0211293.911317.941342.381367.251392.541418.281444.451471.071498.131525.661553.641582.091611.001640.40661078.8661078.81205.6101098.41237.6231119.31272.8831138.71315.6991162.71356.8711189.91387.5591221.21416.5691254.01447.3191291.61478.3691339.71510.5381373.81542.8901401.21572.9931431.81602.4931462.91632.8091493.81664.3761527.21696.8

1639.

96.63% 1670.20679071995M1623.1558.31713.394.76%1700.61.011870760531995M1637.1587.51731.4081681881995M17561617.31762.809121995M1648.41794.6101818771901995M111935.21680.251827.021911995M2389.1713.31859.8125591922,5002,0002,5002,000图3-1：1,500原TX序1,000列500数004080120160200据T通过对《1980-1995年各月社会消费品零售总额（亿元》序列数据图的观察，XEViewsX实用标准文案实用标准文案精彩文案精彩文案的回归拟合。（1）一次幂函数Xt

abRsquared0.7917252,5002,5002,0001,2001,5001,0008005004000-5000-400255075100125150175ResidualActualFitted）二次幂函数Xt

abRsquared0.9082762,5002,5002,0001,0001,5008006001,00040050020000-200-400255075100125150175ResidualActualFitted）三次幂函数Xt

abRsquared0.9445642,5002,5002,0008001,5006001,00040050020000-200-400255075100125150175ResidualActualFitted）四次幂函数Xt

abRsquared0.9480922,5002,5002,0006001,5001,00040050020000-200255075100125150175ResidualActualFitted）五次幂函数Xt

abRsquared0.9366252,5002,5002,0001,5006001,00040050020000-200255075100125150175ResidualActualFittedRsquared4

Rsquared3

Rsquared5

Rsquared2

Rsquared1实用标准文案实用标准文案精彩文案精彩文案X到五次幂函数回归方程。可以确定长期趋势T