Tổng sản phẩm quốc nội Việt Nam giai đoạn 1985-2013 Nguồn số liệu: http://databank.worldbank.org Năm 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 GDP (USD) 14094688429.5982 26336617862.4431 36658108169.2072 25423812494.3469 6293304847.1284 6471740486.3194 9613369553.8511 9866990096.3162 13180954014.0721 16286434094.0188 20736163915.2435 24657470331.5922 26843701136.7260 27209601995.8245 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 49424107709.8946 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.9570 115931749904.8600 135539487317.0080 155820001920.4920 171390003299.3990 Các phương pháp sử dụng để dự báo chuối thời gian là: - Phương pháp san mũ (cụ thể san mũ xu thế): Vì đối tượng dự báo (GDP giai đoạn 1985-2013) xu tuyến tính Tuy nhiên GDP chịu tác động nhiều yếu tố khác nên dễ có phát triển đột biến - Các mô hình thuộc nhóm Box Jenkins: Vì phương pháp đa năng, chi tiết đáng tin cậy, ứng dụng đơn giản, dễ dàng Đồ thị Giả sử dùng phương pháp san mũ để dự báo biến động chuỗi thời gian này, phương pháp san mũ nên sử dụng phương pháp san mũ xu đồ thị vẽ câu 2, đối tượng dự báo thể xu tuyến tính Trong trường hợp dự báo này, ta nên lựa chọn tham số san lớn (trọng số giảm nhanh) đối tượng dự báo có biến động lớn tại, tham số san lớn làm cho quan sát khứ tác động tới giá trị dự báo (α=0,7) 4.Dự báo  Phương pháp ngoại suy: Biểu diễn quan sát chuỗi thời gian hệ toạ độ, nhận thấy hàm xu có dạng tuyến tính: xt=a+bt Năm t Y t2 t*Y2 1985 14094688429.5982 14094688429.5982 1986 26336617862.4431 52673235724.8862 1987 36658108169.2072 109974324507.622 1988 25423812494.3469 16 101695249977.388 1989 6293304847.1284 25 31466524235.6421 1990 6471740486.3194 36 38830442917.9168 1991 9613369553.8511 49 67293586876.9578 1992 9866990096.3162 64 78935920770.5297 1993 13180954014.0721 81 118628586126.649 1994 10 16286434094.0188 100 1995 11 20736163915.2435 121 1996 12 24657470331.5922 144 1997 13 26843701136.726 169 1998 14 27209601995.8245 196 1999 15 28683658004.771 225 2000 16 33640085727.518 256 2001 17 35291349277.3143 289 2002 18 37947904054.452 324 2003 19 42717072777.5838 361 2004 20 49424107709.8946 400 2005 21 57633255739.4104 441 2006 22 66371664817.0436 484 2007 23 77414425532.2452 529 2008 24 99130304099.1274 576 2009 25 106014600963.957 625 2010 26 115931749904.86 676 162864340940.188 228097803067.678 295889643979.106 348968114777.438 380934427941.543 430254870071.565 538241371640.288 599952937714.343 683062272980.136 811624382774.092 988482154197.892 1210298370527.62 00 1460176625974.96 00 1780531787241.64 00 2379127298379.06 00 2650365024098.92 00 3014225497526.36 00 2011 27 135539487317.008 729 2012 28 155820001920.492 784 2013 29 171390003299.399 841 Tổng 435 1476622628571.76 8555 3659566157559.22 00 4362960053773.78 00 4970310095682.57 00 31569525790415.6 Các tham số ước lượng a, b thu thông qua giải hệ phương trình chuẩn => a=-18689266710 ; b= 4640485893 Hàm dự báo: = -18689266710 + 4640485893.t => GDP Việt Nam năm 2014 (t=30) 120525310080 (USD) GDP Việt Nam năm 2015 (t=31) 125165795975 (USD) GDP Việt Nam năm 2016 (t=32) 129806281866 (USD) GDP Việt Nam năm 2017 (t=33) 134446767759 (USD) GDP Việt Nam năm 2018 (t=34) 139087253652 (USD)  Phương pháp san mũ với khoảng san 3: - Xác định giá trị a0 b0 b0 = X2 - X1 = 26336617862.4431 - 14094688429.5982 = 12241929432.8449 a0 = X1 - b0 = 14094688429.5982 - 12241929432.8449 = 1852758996.7533 - Xác định giá trị α giá trị toán tử san sở (năm gốc) α = 2/(m+1) = 2/(3+1)=0.5 • • • • • • Theo phương trình đệ quy: , ta tính toán tử san ước lượng hàm dự báo tất thời điểm sau (trình bày bảng dưới) Hàm dự báo là: 170761863769.1620 + 15998789451.0959*l Theo mô hình dự báo: GDP Việt Nam năm 2014 (l=1) 186760653220.2580 (USD) GDP Việt Nam năm 2015 (l=2) 202759442671.3540 (USD) GDP Việt Nam năm 2016 (l=3) 218758232122.4500 (USD) GDP Việt Nam năm 2017 (l=4) 234757021573.5460 (USD) GDP Việt Nam năm 2018 (l=5) 250755811024.6420 (USD) Năm 1985 Xt 1986 1997 1998 1999 2000 2001 2002 2003 a -10389170436.0916 14094688429.5982 14094688429.5982 1852758996.7533 26336617862.4431 25376398299.4027 25400105396.8748 15846705122.0016 11159222804.1605 10386296179.0058 10126643137.6610 11653798575.8666 13614578648.0780 19507342022.4764 17677023572.2390 14418123188.1998 12402209683.6028 11264426410.6319 11459112493.2492 37138217950.7274 31292868771.2732 14016386671.7642 7900322420.1213 8370382674.4089 8988859864.6901 11848484658.4839 12241929432.844 12241929432.844 11761819651.324 5892763374.3984 -1830318450.2374 -3258900384.0392 -2015913504.5970 -1137783272.9709 194686082.6173 13970116334.9427 12714614414.0960 15225618255.7894 1255501920.8467 12043170741.1012 17353140125.0931 15033877269.5945 19672402980.5917 2319262855.4986 16481120176.6361 21005305228.3426 18019591248.9686 23991019207.7167 2985713979.3741 21991665836.0902 23924503182.5343 20972047215.7515 26876959149.3172 2952455966.7829 26976733187.0908 25567052589.1794 23269549902.4654 27864555275.8934 2297502686.7140 29829415116.1001 27125355296.9752 25197452599.7203 29053257994.2301 1927902697.2549 30162057962.6074 30382720512.2466 27790086555.9835 32975354468.5098 2592633956.2632 30981160691.4850 32837034894.7805 30313560725.3820 35360509064.1789 2523474169.3985 35567988424.7729 35392469474.6162 32853015099.9991 37931923849.2334 2539454374.6171 37883983233.5774 39054771126.1000 35953893113.0496 42155649139.1505 3100878013.0505 40471378223.8505 26336617862.4431 1987 1996 -22631099868.9365 1852758996.7533 1995 S2 14094688429.5982 1988 1989 1990 1991 1992 1993 1994 S1 -10389170436.0916 t 36658108169.2072 1 1 25423812494.3469 6293304847.1284 6471740486.3194 9613369553.8511 9866990096.3162 13180954014.0721 16286434094.0188 b 26336617862.4431 38578547295.2880 48900037602.0521 37185632145.6716 12186068221.5268 4641422036.0821 6354469169.8119 7851076591.7192 20736163915.2435 24657470331.5922 26843701136.7260 27209601995.8245 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2 2 3 3 3 49424107709.8946 44239439417.9973 40096666265.5234 48382212570.4712 4142773152.4739 45256527152.2009 50936347578.7039 45516506922.1136 56356188235.2941 5419840656.5902 52524985722.9451 58654006197.8737 52085256559.9937 65222755835.7538 6568749637.8800 61776028891.8843 68034215865.0595 60059736212.5266 76008695517.5923 71791505473.6338 83582259982.0934 71820998097.3100 95343521866.8769 94798430473.0252 105365090188.943 120452288752.975 138136145336.734 154763074318.066 83309714285.1676 106287146660.8830 94337402237.0551 107394845495.015 122765495415.874 138764284866.970 116392778140.8300 7974479652.5329 11761261884.783 11488716187.857 11027687951.887 13057443257.960 15370649920.859 15998789451.095 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.957 115931749904.860 135539487317.008 155820001920.492 171390003299.399 133509732010.9350 153506795257.5930 170761863769.1620 83983175170.1252 107104783751.6600 117775862848.7400 127420466092.7180 146567175268.8960 168877445178.452 186760653220.2580 202759442671.3540 218758232122.4500 234757021573.5460 250755811024.6420  Trung bình trượt với khoảng trượt 5: Năm 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 t 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 GDP (USD) 14094688429.5982 26336617862.4431 36658108169.2072 25423812494.3469 6293304847.1284 6471740486.3194 9613369553.8511 9866990096.3162 13180954014.0721 16286434094.0188 20736163915.2435 24657470331.5922 26843701136.7260 27209601995.8245 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 49424107709.8946 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.957 21761306360.5448 20236716771.8890 16892067110.1706 11533843495.5924 9085271799.5375 11083897648.9155 13936782334.7003 16945602490.2486 20340944698.3305 23146674294.6810 25626119076.8314 28206903439.2863 30333679228.4308 32554519811.9760 35656013968.3278 39804103909.3525 44602737911.7310 50818801019.6769 58712105315.2355 69994751579.5442 81312850230.3567 21761306360.5448 20236716771.8890 16892067110.1706 11533843495.5924 9085271799.5375 11083897648.9155 13936782334.7003 16945602490.2486 20340944698.3305 23146674294.6810 25626119076.8314 28206903439.2863 30333679228.4308 32554519811.9760 35656013968.3278 39804103909.3525 44602737911.7310 50818801019.6769 58712105315.2355 69994751579.5442 2010 2011 2012 2013 2014 2015 2016 2017 2018 26 27 28 29 30 31 32 33 115931749904.860 135539487317.008 155820001920.492 171390003299.399 136939168681.143 143124082224.580 148562548688.525 151167160962.828 34 92972549063.4466 106806113563.440 122487228841.089 136939168681.143 143124082224.580 148562548688.525 151167160962.828 150236592771.295 81312850230.3567 92972549063.4466 106806113563.4400 122487228841.0890 136939168681.1430 143124082224.5800 148562548688.5250 151167160962.8280 150236592771.2950 (Vì từ năm 2014 giá trị thực GDP nên để dự báo cho năm 2015 đến năm 2018, ta coi giá trị dự báo giá trị thực GDP)  Mô hình ARIMA (2,0,0) Để ước lượng tham số ta phải giải hệ phương trình: Tính toán phần tử từ bảng số dưới, thay vào ta được: => Mô hình ARIMA(2,0,0): GDP Việt Nam: Y2014 = -652662314.7 + 1.3923Y2013 - 0.2991Y2012 = 191367876704.6340 (USD) Y2015 = -652662314.7 + 1.3923Y2014 - 0.2991Y2013 = 214526082434.3120 (USD) Y2016 = -652662314.7 + 1.3923Y2015 - 0.2991Y2014 = 240793870336.2360 (USD) Y2017 = -652662314.7 + 1.3923Y2016 - 0.2991Y2015 = 270439892098.3390 (USD) Y2018 = -652662314.7 + 1.3923Y2017 - 0.2991Y2016 = 303859352836.2490 (USD) (Vì từ năm 2014 giá trị thực GDP nên để dự báo cho năm 2015 đến năm 2018, ta coi giá trị dự báo giá trị thực GDP) Năm 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Tổng Y 14094688429.5982 26336617862.4431 36658108169.2072 25423812494.3469 6293304847.1284 6471740486.3194 9613369553.8511 9866990096.3162 13180954014.0721 16286434094.0188 20736163915.2435 24657470331.5922 26843701136.7260 27209601995.8245 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 49424107709.8946 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.9570 115931749904.8600 135539487317.0080 155820001920.4920 171390003299.3990 1436191322279.7200 Yt-1 Yt-2 14094688429.5982 26336617862.4431 14094688429.5982 36658108169.2072 26336617862.4431 25423812494.3469 36658108169.2072 6293304847.1284 25423812494.3469 6471740486.3194 6293304847.1284 9613369553.8511 6471740486.3194 9866990096.3162 9613369553.8511 13180954014.0721 9866990096.3162 16286434094.0188 13180954014.0721 20736163915.2435 16286434094.0188 24657470331.5922 20736163915.2435 26843701136.7260 24657470331.5922 27209601995.8245 26843701136.7260 28683658004.7710 27209601995.8245 33640085727.5180 28683658004.7710 35291349277.3143 33640085727.5180 37947904054.4520 35291349277.3143 42717072777.5838 37947904054.4520 49424107709.8946 42717072777.5838 57633255739.4104 49424107709.8946 66371664817.0436 57633255739.4104 77414425532.2452 66371664817.0436 99130304099.1274 77414425532.2452 106014600963.9570 99130304099.1274 115931749904.8600 106014600963.9570 135539487317.0080 115931749904.8600 155820001920.4920 135539487317.0080 1291137936842.7700 1149412623351.8700 Yt-12 693617440432357000000 1343816894545300000000 646370241747710000000 39605685898889800000 41883424922265700000 92416874178911300000 97357493560802000000 173737548721083000000 265247935498818000000 429988493919847000000 607990843153350000000 720584290717865000000 740362440771177000000 822752236534663000000 1131655367754760000000 1245479333813390000000 1440043422125890000000 1824748306685390000000 2442742422919260000000 3321592167124280000000 4405197890585980000000 5992993280487540000000 9826817190785470000000 11239095617547000000000 13440170636003000000000 18370952622157400000000 24279872998502100000000 105677093101095000000000 Yt-22 198660241927449000000 693617440432357000000 1343816894545300000000 646370241747710000000 39605685898889800000 41883424922265700000 92416874178911300000 97357493560802000000 173737548721083000000 265247935498818000000 429988493919847000000 607990843153350000000 720584290717865000000 740362440771177000000 822752236534663000000 1131655367754760000000 1245479333813390000000 1440043422125890000000 1824748306685390000000 2442742422919260000000 3321592167124280000000 4405197890585980000000 5992993280487540000000 9826817190785470000000 11239095617547000000000 13440170636003000000000 18370952622157400000000 81595880344519900000000 Yt-1Yt-2 YtYt-1 YtYt-2 371206423060526000000 965450586412514000000 931988868491410000000 159999802403157000000 40728635771911000000 62215232951608400000 94855022180076500000 130056342716849000000 214670738846478000000 337718166968384000000 511301346531149000000 661897764368949000000 730406424025176000000 780470918094164000000 964920714259304000000 1187204015128630000000 1339232736327680000000 1621023379250790000000 2111253206010710000000 2848472239336520000000 3825215132251100000000 5138124303430160000000 7674115544670720000000 10509259632504700000000 12290458205217000000000 15713329945868300000000 21119763174038700000000 92335338501116700000000 965450586412514000000 931988868491410000000 159999802403157000000 40728635771911000000 62215232951608400000 94855022180076500000 130056342716849000000 214670738846478000000 337718166968384000000 511301346531149000000 661897764368949000000 730406424025176000000 780470918094164000000 964920714259304000000 1187204015128630000000 1339232736327680000000 1621023379250790000000 2111253206010710000000 2848472239336520000000 3825215132251100000000 5138124303430160000000 7674115544670720000000 10509259632504700000000 12290458205217000000000 15713329945868300000000 21119763174038700000000 26705990643265500000000 118670122721322000000000 516684613063484000000 669577234270021000000 230700649827829000000 164536316636258000000 60499865210487700000 63856599284442100000 126713382009592000000 160698083909990000000 273322422995086000000 401582265480700000000 556635386862959000000 670919953946475000000 769975542988131000000 915333343751181000000 1012284993197410000000 1276570745571390000000 1507543135498160000000 1875541297351980000000 2461923979829490000000 3280360310802580000000 4461645384619430000000 6579443316878890000000 8207059431654940000000 11492349622812800000000 14369164662771900000000 18064485492821300000000 23230113178460800000000 103399521212508000000000 Tính giá trị đo lường độ xác dự báo:  Phương pháp ngoại suy: y y14094688429.5982 26336617862.4431 36658108169.2072 25423812494.3469 6293304847.1284 6471740486.3195 9613369553.8511 9866990096.3162 13180954014.0721 16286434094.0188 20736163915.2435 24657470331.5922 26843701136.7260 27209601995.8245 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 49424107709.8946 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.9570 115931749904.8600 135539487317.0080 155820001920.4920 171390003299.3990 Tổng -14048780817 -9408294924 -4767809031 -127323138 4513162755 9153648648 13794134541 18434620434 23075106327 27715592220 32356078113 36996564006 41637049899 46277535792 50918021685 55558507578 60198993471 64839479364 69479965257 74120451150 78760937043 83401422936 88041908829 92682394722 97322880615 101963366508 106603852401 111244338294 115884824187 28143469246.5982 35744912786.4431 41425917200.2072 25551135632.3469 1780142092.1284 -2681908161.6805 -4180764987.1489 -8567630337.6838 -9894152312.9279 -11429158125.9812 -11619914197.7565 -12339093674.4078 -14793348762.2740 -19067933796.1755 -22234363680.2290 -21918421850.4820 -24907644193.6857 -26891575309.5480 -26762892479.4162 -24696343440.1054 -21127681303.5896 -17029758118.9564 -10627483296.7548 6447909377.1274 8691720348.9570 13968383396.8600 28935634916.0080 44575663626.4920 55505179112.3990 -293.2360 |y- (y-)2 28143469246.5982 35744912786.4431 41425917200.2072 25551135632.3469 1780142092.1284 2681908161.6805 4180764987.1489 8567630337.6838 9894152312.9279 11429158125.9812 11619914197.7565 12339093674.4078 14793348762.2740 19067933796.1755 22234363680.2290 21918421850.4820 24907644193.6857 26891575309.5480 26762892479.4162 24696343440.1054 21127681303.5896 17029758118.9564 10627483296.7548 6447909377.1274 8691720348.9570 13968383396.8600 28935634916.0080 44575663626.4920 55505179112.3990 581540135764.3700 792054861234219000000 1277698790110420000000 1716106615878420000000 652860532102587000000 3168905868167350000 7192631387688690000 17478795877770100000 73404289603199700000 97894249991416500000 130625655468682000000 135022405963223000000 152253232705811000000 218843167602274000000 363586099255332000000 494366928264686000000 480417216415687000000 620390739279245000000 723156822629091000000 716252413864792000000 609909379311637000000 446378917266050000000 290012661590161000000 112943401222802000000 41575535335647400000 75546002624473200000 195115734721674000000 837270967992501000000 1986989787742160000000 3080824908299490000000 16349341649609300000000 x100 199.67 135.72 113.01 100.50 28.29 -41.44 -43.49 -86.83 -75.06 -70.18 -56.04 -50.04 -55.11 -70.08 -77.52 -65.16 -70.58 -70.86 -62.65 -49.97 -36.66 -25.66 -13.73 6.50 8.20 12.05 21.35 28.61 32.39 x100 199.67 135.72 113.01 100.50 28.29 41.44 43.49 86.83 75.06 70.18 56.04 50.04 55.11 70.08 77.52 65.16 70.58 70.86 62.65 49.97 36.66 25.66 13.73 6.50 8.20 12.05 21.35 28.61 32.39 1707.3282 => MFE = = = -10.1116 MAE = = = 20053108129.8059 MSE = = = 563770401710666000000 MAPE = = = 58.87 (%)  Phương pháp san mũ với khoảng san 3: y 14094688429.5982 26336617862.4431 36658108169.2072 25423812494.3469 6293304847.1284 6471740486.3195 9613369553.8511 9866990096.3162 13180954014.0721 16286434094.0188 20736163915.2435 24657470331.5922 26843701136.7260 27209601995.8245 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 49424107709.8946 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.957 (y-)2 y26336617862.4431 38578547295.2880 48900037602.0521 37185632145.6716 12186068221.5268 4641422036.0821 6354469169.8119 7851076591.7192 12043170741.1012 16481120176.6361 21991665836.0902 26976733187.0908 29829415116.1001 30162057962.6074 30981160691.4850 35567988424.7729 37883983233.5774 40471378223.8505 45256527152.2009 52524985722.9451 61776028891.8843 71791505473.6338 83983175170.1252 107104783751.660 |y- x100 x100 0.0000 -1920439126.0808 -23476225107.7052 -30892327298.5432 -5714327735.2074 4971947517.7691 3512520926.5043 5329877422.3529 4243263352.9176 4255043738.6074 2665804495.5020 -133032050.3648 -2619813120.2756 -1478399957.8364 2658925036.0330 -276639147.4586 63920820.8746 2245694553.7333 4167580557.6937 5108270016.4653 4595635925.1593 5622920058.6114 15147128929.0022 0.0000 1920439126.0808 23476225107.7052 30892327298.5432 5714327735.2074 4971947517.7691 3512520926.5043 5329877422.3529 4243263352.9176 4255043738.6074 2665804495.5020 133032050.3648 2619813120.2756 1478399957.8364 2658925036.0330 276639147.4586 63920820.8746 2245694553.7333 4167580557.6937 5108270016.4653 4595635925.1593 5622920058.6114 15147128929.0022 3688086436982000000 551133145307648000000 954335885920316000000 32653541465360000000 24720262119449800000 12337803259130900000 28407593337306800000 18005283882213400000 18105397217461800000 7106513608238540000 17697526424253400 6863420785168000000 2185666435330600000 7069882347243220000 76529217906618400 4085871341278240 5043144028667440000 17368727704866200000 26094422561118800000 21119869556615000000 31617229985534100000 229435514791814000000 0.00 -5.24 -92.34 -490.88 -88.30 51.72 35.60 40.44 26.05 20.52 10.81 -0.50 -9.63 -5.15 7.90 -0.78 0.17 5.26 8.43 8.86 6.92 7.26 15.28 0.00 5.24 92.34 490.88 88.30 51.72 35.60 40.44 26.05 20.52 10.81 0.50 9.63 5.15 7.90 0.78 0.17 5.26 8.43 8.86 6.92 7.26 15.28 -1090182787.7033 1090182787.7033 1188498510604520000 -1.03 1.03 115931749904.860 135539487317.008 155820001920.492 171390003299.399 Tổng 117775862848.740 127420466092.718 146567175268.896 168877445178.452 -1844112943.8804 1844112943.8804 3400752549787300000 -1.59 1.59 8119021224.2904 8119021224.2904 65918505640478100000 5.99 5.99 9252826651.5965 9252826651.5965 85614801044494400000 5.94 5.94 2512558120.9469 15027440073.0042 2512558120.9469 153918438623.1150 6312948311136210000 2159825209422640000000 1.47 1.47 954.0582 => MFE = = = 518187588.7243 MAE = = = 5307532366.3143 MSE = = = 74476731359401300000 MAPE = = = 32.9 (%)  Phương pháp trung bình trượt với khoảng trượt y y14094688429.5982 26336617862.4431 36658108169.2072 25423812494.3469 6293304847.1284 6471740486.3195 21761306360.5448 -15289565874.2253 9613369553.8511 20236716771.8890 -10623347218.0379 9866990096.3162 16892067110.1706 -7025077013.8544 13180954014.0721 11533843495.5924 1647110518.4797 16286434094.0188 9085271799.5375 7201162294.4813 20736163915.2435 11083897648.9155 9652266266.3280 24657470331.5922 13936782334.7003 10720687996.8919 26843701136.7260 16945602490.2486 9898098646.4774 27209601995.8245 20340944698.3305 6868657297.4940 |y- 15289565874.2253 10623347218.0379 7025077013.8544 1647110518.4797 7201162294.4813 9652266266.3280 10720687996.8919 9898098646.4774 6868657297.4940 (y-)2 233770824622275000000 112855506114994000000 49351707050585600000 2712973060086400000 51856738391459800000 93166244076092800000 114933151126701000000 97972356815398500000 47178453070417300000 x100 -236.25 -110.51 -71.20 12.50 44.22 46.55 43.48 36.87 25.24 x100 236.25 110.51 71.20 12.50 44.22 46.55 43.48 36.87 25.24 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 49424107709.8946 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.9570 115931749904.8600 135539487317.0080 155820001920.4920 171390003299.3990 Tổng 23146674294.6810 25626119076.8314 28206903439.2863 30333679228.4308 32554519811.9760 35656013968.3278 39804103909.3525 44602737911.7310 50818801019.6769 58712105315.2355 69994751579.5442 81312850230.3567 92972549063.4466 106806113563.4400 122487228841.0890 5536983710.0900 8013966650.6866 7084445838.0280 7614224826.0212 10162552965.6078 13768093741.5668 17829151830.0579 21768926905.3126 26595624512.5683 40418198783.8919 36019849384.4128 34618899674.5033 42566938253.5614 49013888357.0525 48902774458.3101 382964512805.7060 5536983710.0900 8013966650.6866 7084445838.0280 7614224826.0212 10162552965.6078 13768093741.5668 17829151830.0579 21768926905.3126 26595624512.5683 40418198783.8919 36019849384.4128 34618899674.5033 42566938253.5614 49013888357.0525 48902774458.3101 448840493017.9410 30658188605802000000 64223661478316400000 50189372831951700000 57976419701198200000 103277482778785000000 189560405276570000000 317878654979256000000 473886178608842000000 707327243213525000000 1633630792934200000000 1297429549675780000000 1198468214673320000000 1811944232282510000000 2402361251877610000000 2391481349720350000000 13534090952966000000000 19.30 23.82 20.07 20.06 23.79 27.86 30.94 32.80 34.35 40.77 33.98 29.86 31.41 31.46 28.53 219.90 19.30 23.82 20.07 20.06 23.79 27.86 30.94 32.80 34.35 40.77 33.98 29.86 31.41 31.46 28.53 1055.81 => MFE = = = 15956854700.2377 MAE = = = 18701687209.0809 MSE = = = 563920456373584000000 MAPE = = = 43.99 (%)  Mô hình ARIMA(2,0,0) y 14094688429.5982 26336617862.4431 36658108169.2072 31800089425.8867 y- 4858018743.3205 |y- 4858018743.3205 (y-)2 23600346110453100000 x100 13.25 x100 13.25 25423812494.3469 6293304847.1284 6471740486.3194 9613369553.8511 9866990096.3162 13180954014.0721 16286434094.0188 20736163915.2435 24657470331.5922 26843701136.7260 27209601995.8245 28683658004.7710 33640085727.5180 35291349277.3143 37947904054.4520 42717072777.5838 49424107709.8946 57633255739.4104 66371664817.0436 77414425532.2452 99130304099.1274 106014600963.957 115931749904.860 135539487317.008 155820001920.492 171390003299.399 Tổng 42509139286.6305 23780471667.7693 505243706.8977 6475614484.6264 10796334535.6688 10209789162.8442 14747963221.2844 18080516528.7934 23347026266.9725 27475747000.9265 29346773401.7844 29202315534.0917 31145202768.3916 37605146934.4963 38421733643.0041 41626561931.4688 47472100010.8433 55383846382.0109 64807369035.2516 74518499818.4122 87279677407.0672 114211805405.821 117301592651.368 129050145929.517 153383779480.227 175755665702.684 -17085326792.2836 -17487166820.6409 5966496779.4217 3137755069.2247 -929344439.3526 2971164851.2279 1538470872.7344 2655647386.4501 1310444064.6197 -632045864.2005 -2137171405.9599 -518657529.3207 2494882959.1264 -2313797657.1820 -473829588.5521 1090510846.1150 1952007699.0513 2249409357.3995 1564295781.7920 2895925713.8330 11850626692.0602 17085326792.2836 17487166820.6409 5966496779.4217 3137755069.2247 929344439.3526 2971164851.2279 1538470872.7344 2655647386.4501 1310444064.6197 632045864.2005 2137171405.9599 518657529.3207 2494882959.1264 2313797657.1820 473829588.5521 1090510846.1150 1952007699.0513 2249409357.3995 1564295781.7920 2895925713.8330 11850626692.0602 291908391599123000000 305801003412925000000 35599083818849300000 9845506874445330000 863681086955517000 8827820573172220000 2366892626252110000 7052463041159190000 1717263646496990000 399481974452943000 4567501618452570000 269005632721062000 6224440979739510000 5353659598380980000 224514478987425000 1189213905494400000 3810334057155400000 5059842457156250000 2447021292932120000 8386385740039390000 140437352994569000000 -67.20 -277.87 92.19 32.64 -9.42 22.54 9.45 12.81 5.31 -2.35 -7.85 -1.81 7.42 -6.56 -1.25 2.55 3.95 3.90 2.36 3.74 11.95 67.20 277.87 92.19 32.64 9.42 22.54 9.45 12.81 5.31 2.35 7.85 1.81 7.42 6.56 1.25 2.55 3.95 3.90 2.36 3.74 11.95 -8197204441.8636 8197204441.8636 67194160661707600000 -7.73 7.73 -1369842746.5083 1369842746.5083 1876469150161450000 -1.18 1.18 6489341387.4910 6489341387.4910 42111551643403000000 4.79 4.79 2436222440.2654 2436222440.2654 5935179778452610000 1.56 1.56 -4365662403.2849 -48829045.0164 4365662403.2849 110971270333.2820 19059008219455700000 1002127576973090000000 -2.55 2.55 616.19 => MFE = = = -1808483.1488 MAE = = = 4110047049.3808 MSE = = = 37115836184188600000 MAPE = = = 22.82 (%) Phương pháp dự báo thích hợp cho chuỗi thời gian phương pháp Box Jenkins (trong sử dụng mô hình ARIMA(2,0,0)) phương pháp theo lý thuyết sử dụng cho dự báo ngắn hạn theo tính toán câu 5, phương pháp có sai số dự báo nhỏ Hơn nữa, phương pháp có ứng dụng đơn giản, dễ dàng thực để dự báo