Chinese Journal of Management Science ›› 2024, Vol. 32 ›› Issue (9): 48-58.doi: 10.16381/j.cnki.issn1003-207x.2021.0610
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Yunjie Mei1,Xiangyan Zeng1(),Shuli Yan2
Received:
2021-03-29
Revised:
2022-04-15
Online:
2024-09-25
Published:
2024-10-12
Contact:
Xiangyan Zeng
E-mail:zengxyhbyc@163.com
CLC Number:
Yunjie Mei,Xiangyan Zeng,Shuli Yan. A Matrix Autoregressive Time-delay Grey Multivariable Model for Three-parameter Interval Grey Number Sequences[J]. Chinese Journal of Management Science, 2024, 32(9): 48-58.
"
年份 | 原序列 | MARGM(1,N) | MTIGM(1,1) |
---|---|---|---|
拟合值 | |||
2000 | [9547.8, 11415.9, 13102.0] | [9547.8, 11415.9, 13102.0] | [9547.8, 11415.9, 13102.0] |
2001 | [10641.4, 12414.9, 13915.4] | [10691.4, 12469.0, 13991.0] | [11539.7, 13808.1, 15814.1] |
2002 | [11319.7, 13526.0, 15460.6] | [11848.8, 13932.3, 15812.6] | [12267.4, 14667.5, 16800.9] |
2003 | [13146.2, 15674.0, 18031.6] | [12790.2, 15643.7, 18221.3] | [13450.2, 16145.9, 18553.5] |
2004 | [15292.1, 18571.3, 21535.5] | [15104.9, 18531.5, 21350.4] | [15274.5, 18420.1 21230.1] |
2005 | [18159.0, 22020.6, 25723.9] | [18040.7, 21911.2, 25362.1] | [17843.0, 21648.0, 25041.4] |
2006 | [21418.2, 26089.8, 30429.8] | [21705.2, 26375.1, 30693.7] | [20974.5, 25609.3, 29738.8] |
2007 | [25983.1, 31657.7, 36861.1] | [26043.7, 31881.9, 37165.8] | [25031.1, 30630.1, 35593.4] |
2008 | [31613.2, 37488.3, 41196.4] | [31041.0, 36229.9, 40175.9] | [29273.5, 35182.1, 40309.3] |
2009 | [32594.0, 40042.2, 46928.2] | [21503.2, 39845.5, 46699.5] | [34679.8, 41146.1, 46636.9] |
2010 | [39364.2, 47906.6, 55933.6] | [39846.4, 48476.1, 56528.1] | [41302.2, 49370.3, 56242.3] |
2011 | [47194.0, 56758.8,64334.6] | [47128.3, 56617.4, 64177.5] | [48055.9, 57299.3, 56242.3] |
2012 | [52316.2, 61159.8, 68633.5] | [52408.1, 61509.3, 68972.0] | [52394.5, 62066.7, 70240.1] |
2013 | [55861.2, 65487.9, 74211.4] | [55463.0, 65170.2, 73822.2] | [54032.6, 64124.5, 72800.5] |
2014 | [59127.4, 69320.7, 77725.9] | [59232.5, 69441.3, 77820.6] | [56203.6, 66712.5, 75868.0] |
2015 | [60505.9, 70334.7, 78356.3] | [60861.3, 70824.3, 78824.3] | [57966.5, 68461.7, 77683.5] |
2016 | [61106.8, 73857.0, 85504.1] | [61005.3, 73512.1, 85288.3] | [62766.0, 74196.9, 84292.9] |
2017 | [69315.5, 82895.2, 95368.0] | [68985.7, 82509.1, 94923.8] | [70664.4, 84067.0, 95940.9] |
2018 | [76598.2, 91208.8, 104023.9] | [76811.6, 91534.3, 104344.7] | [77792.1, 92858.0, 106259.6] |
2019 | [80596.7, 95167.7, 107730.1] | [84142.8, 99794.1, 114270.2] | [85939.5, 102731.5, 117692.3] |
2020 | [72533.4, 96063.8, 113939.9] | [93147.8, 10598.8, 126121.1] | [95934.1, 114912.6, 131831.1] |
"
年份 | ARGM(1,N) | GM(1,N) | GM(1,1) |
---|---|---|---|
拟合值 | |||
2000 | [9547.8, 11415.9, 13102.0] | [9547.8, 11415.9, 13102.0] | [9547.8, 11415.9, 13102.0] |
2001 | [10688.5, 12864.7, 14740.5] | [-150, -336.7, -124.7] | [15226.8, 18253.0, 20822.8] |
2002 | [13643.8, 15744.9, 17488.9] | [1525.8, 1541.3, 1999.2] | [16327.4, 19543.1, 22279.9] |
2003 | [14076.3, 16615.5, 18947.7] | [3261.9, 3629.2, 4362.8] | [17553.6, 20995.4, 23941.2] |
2004 | [13643.8, 14076.3, 15868.8] | [5310.3, 6035.4, 7090.4] | [18978.9, 22698.5, 25903.8] |
2005 | [18174.7, 21952.7, 25461.1] | [7764.4, 9172.4, 10620.6] | [20655.3, 24717.3, 28247.9] |
2006 | [21194.7, 25579.1, 29900.2] | [10860.9, 13053.0, 14974.1] | [22638.8,27110.1, 31033.3] |
2007 | [24798.2, 30169.2, 35222.2] | [14378.8, 17288.3, 19759.1] | [25014.5, 29982.1, 34371.0] |
2008 | [29954.5, 36427.7, 42229.8] | [18673.0, 22622.0, 25762.2] | [27901.0, 33421.0, 38242.8] |
2009 | [35987.1, 42575.9, 46519.3] | [24271.3, 29198.3, 33114.1] | [31116.7, 37276.9, 42614.0] |
2010 | [36303.8, 44544.8, 52155.5] | [29415.0, 35599.9, 40350.9] | [34720.7, 41651.0,47716.1] |
2011 | [43114.5, 52736.6, 61704.4] | [35816.2, 43376.7, 49128.3] | [39058.8, 46856.4, 53681.7] |
2012 | [51695.1, 62381.0, 70501.6] | [43852.0, 52841.7, 59750.4] | [44046.0, 52721.0, 60277.2] |
2013 | [56767.2, 66309.8, 74184.6] | [52126.4, 62091.3, 70203.9] | [49467.5, 59019.7, 67362.6] |
2014 | [59417.7, 69615.5, 79055.9] | [60142.6, 71154.9, 80515.9] | [55230.4, 65724.3, 74899.0] |
2015 | [62152.0,73206.1, 82475.4] | [67325.4, 79145.8, 89741.1] | [61226.1, 72669.9, 82640.9] |
2016 | [63970.3, 74408.7, 83180.7] | [72463.7, 85177.1, 96952.7] | [67321.0, 79841.2, 90768.7] |
2017 | [65808.3, 7981.5, 92408.0] | [76076.9, 90432.1, 103435.2] | [73857.4, 87637.1, 99740.4] |
2018 | [77895.7, 92840.9, 106262.0] | [80473.1, 96575.4, 110956.2] | [81170.2, 96296.0, 109630.6] |
2019 | [88301.0, 104172.9, 117668.4] | [87898.2, 106890.7, 158062.3] | [89494.3, 106109.5, 120781.4] |
2020 | [101913.3, 119368.7, 133729.5] | [97976.7, 122487.4, 227064.4] | [98938.0,117216.4, 133388.7] |
"
模型 | MARGM(1,N) | MTIGM(1,1) | ARGM(1,N) | GM (1,N) | GM (1,1) |
---|---|---|---|---|---|
拟合MAPE(%) | 0.86 | 3.23 | 4.14 | 37.12 | 14.81 |
拟合MAE | 296.37 | 1141.53 | 1582.19 | 10406.69 | 4714.17 |
拟合RMSE | 87.07 | 316.00 | 470.66 | 2596.35 | 1234.52 |
预测MAPE(%) | 11.60 | 15.23 | 18.40 | 38.33 | 18.36 |
预测MAE | 10340.55 | 13834.91 | 16520.35 | 39058.00 | 16649.46 |
预测RMSE | 8332.77 | 10798.40 | 12917.05 | 29865.64 | 12516.75 |
总体MAPE(%) | 1.94 | 4.43 | 5.56 | 37.24 | 15.16 |
总体MAE | 1300.78 | 2410.87 | 3076.01 | 13271.82 | 5907.50 |
总体RMSE | 837.30 | 1116.74 | 1360.30 | 3959.48 | 1678.79 |
"
年份 | 原序列 | MARGM(1,N) | MTIGM(1,1) |
---|---|---|---|
拟合值 | |||
2002 | [12502.1, 12855.8, 13584.2] | [12502.1, 12855.8, 13584.2] | [12502.1, 12855.8, 13584.2] |
2003 | [13870.6, 14439.0, 15481.4] | [13693.1, 14329.7, 15245.5] | [13325.9, 13974.8, 15267.1] |
2004 | [16124.3, 16662.7, 17524.6] | [16475.4, 16895.4, 18016.3] | [16163.9, 16833.6, 18215.4] |
2005 | [18746.0, 19357.5, 20344.5] | [18792.3, 19391.4, 20431.7] | [19423.3, 20052.4, 21044.9] |
2006 | [22190.4, 22940.6, 24575. 3] | [22201.3, 23040.2, 24773.9] | [22882.7, 23661.7, 25066.1] |
2007 | [27703.2, 28946.9, 31469.8] | [27462.7, 28671.0, 30877.9] | [27198.0, 28140.8, 29810.7] |
2008 | [33392.9, 34206.9, 36062.5] | [33312.7, 34143.6, 35874.0] | [32455.5, 33742.9, 36326.0] |
2009 | [37065.4, 38691.3, 41541.7] | [36952.5, 38571.2, 41440.8] | [38262.4, 39623.5, 42116.9] |
2010 | [43311.1, 45515.5, 49187.8] | [43526.4, 45723.6, 49428.1] | [43808.0, 45413.1, 48114.8] |
2011 | [51683.2, 54030.9, 57487.8] | [51555.4, 53929.5, 57490.9] | [50434.1, 52661.8, 56580.9] |
2012 | [58595.5, 61214.1, 65107.2] | [58686.2, 61260.1, 65045.0] | [58157.3, 60946.9, 65232.1] |
2013 | [66719.3, 69495.9, 73696.6] | [66773.5, 69595.4, 73985.3] | [66288.1, 69432.5, 73571.8] |
2014 | [74492.4, 77663.5, 82580.9] | [74326.4, 77514.2, 82247.7] | [75111.2, 78706.5, 83881.3] |
2015 | [83258.8, 87436.2, 92840.6] | [83575.8, 87715.0, 93353.3] | [83754.3, 87736.5, 93639.0] |
2016 | [92990.5, 97707.0, 104334.0] | [92871.9, 97556.4, 104073.6] | [93369.5, 97897.9, 103750.6] |
2017 | [104346.3, 109589.0, 117067.8] | [104237.7, 109516.8, 116934.0] | [103940.5, 109021.2, 116356.0] |
2018 | [116861.8, 122425.2, 129846.2] | [116908.3, 122468.5, 129920.8] | [116776.9, 122476.0, 130174.9] |
2019 | [127803.3, 133842.8, 141603.5] | [129161.8, 134103.6, 136560.5] | [131135.7, 137154.6, 144606.1] |
2020 | [123008.5, 138494.2, 152727.6] | [123691.6, 130557.4, 151822.6] | [148255.4, 154384.5, 160888.3] |
"
年份 | ARGM(1,N) | GM(1,N) | GM(1,1) |
---|---|---|---|
拟合值 | |||
2002 | [12502.1, 12855.8, 13584.2] | [12502.1, 12855.8, 13584.2] | [12502.1, 12855.8, 13584.2] |
2003 | [13325.9, 13974.8, 15267.1] | [7565.1, 8304.7, 8479.5] | [17580.0, 18241.2, 19508.1] |
2004 | [16163.9, 16833.6, 18215.4] | [11425.3, 12152.1, 12622.8] | [19527.5, 20273.8, 21659.6] |
2005 | [19423.3, 20052.4, 21044.9] | [15540.1, 16380.0, 17127.7] | [21791.4, 22627.8, 24128.1] |
2006 | [22882.7, 23661.7, 25066.1] | [20187.9, 21210.5, 22480.5] | [24449.2, 25392.1, 27056.2] |
2007 | [27198.0, 28140.8, 29810.7] | [25190.9, 26210.1, 27518.6] | [27688.5, 28783.1, 30709.5] |
2008 | [32455.5, 33742.9, 36326.0] | [30559.1, 31585.3, 33486.9] | [31655.2, 32910.4, 35111.5] |
2009 | [38262.4, 39623.5, 42116.9] | [36376.0, 37515.4, 40160.9] | [36229.6, 37674.5, 40170.1] |
2010 | [43808.0, 45413.1, 48114.8] | [43343.9, 44931.4, 47271.7] | [41448.1, 43177.6, 46084.3] |
2011 | [50434.1, 52661.8, 56580.9] | [51296.7, 53324.5, 56984.8] | [47615.5, 49683.2, 53037.9] |
2012 | [58157.3, 60946.9, 65232.1] | [59721.0, 62167.3, 66348.9] | [54775.5, 49683.2, 53037.9] |
2013 | [66288.1, 69432.5, 73571.8] | [68769.3, 71606.2, 75600.9] | [62911.4, 65757.0, 70077.2] |
2014 | [75111.2, 78706.5, 83881.3] | [77770.7, 81187.9, 87559.9] | [72079.5, 75374.3, 80264.1] |
2015 | [83754.3, 87736.5, 93639.0] | [86493.7, 90854.1, 97537.1] | [82321.4, 86164.0, 91698.9] |
2016 | [99369.5, 109021.2, 116356.0] | [95338.8, 100408.7, 106189.4] | [93764.4, 98263.6, 104551.6] |
2017 | [103940.5, 109021.2, 116356.0] | [104178.0, 109896.8, 116943.1] | [106575.4, 111810.9, 118983.7] |
2018 | [116776.9, 122476.0, 130174.9] | [111815.1, 116788.0, 124128.5] | [120938.3, 126973.7, 135078.7] |
2019 | [131135.7, 137154.6, 144606.1] | [122046.7, 128355.3, 134240.4] | [137339.3, 144412.2, 153551.9] |
2020 | [148255.4, 154284.5, 160888.3] | [128810.3, 134295.6, 138785.6] | [156536.3, 164607.4, 174966.3] |
"
模型 | MARGM(1,N) | MTIGM(1,1) | ARGM(1,N) | GM (1,N) | GM (1,1) |
---|---|---|---|---|---|
预测MAPE(%) | 0.49 | 1.42 | 1.57 | 8.84 | 7.44 |
预测MAE | 170.05 | 500.77 | 582.24 | 2704.40 | 2572.98 |
预测RMSE | 51.07 | 154.69 | 172.76 | 811.13 | 729.42 |
拟合MAPE(%) | 1.95 | 5.36 | 7.42 | 5.11 | 14.09 |
拟合MAE | 2697.85 | 7094.79 | 9824.12 | 7091.57 | 19007.26 |
拟合RMSE | 2430.86 | 6254.17 | 8398.86 | 5141.55 | 14717.37 |
总体MAPE(%) | 0.65 | 1.52 | 2.22 | 8.43 | 8.18 |
总体MAE | 515.38 | 1196.10 | 1827.41 | 1829.80 | 3284.57 |
总体RMSE | 275.64 | 633.21 | 949.41 | 929.60 | 1762.53 |
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