extending the logistic model for mortality forecasting and the application of mortality-linked...
TRANSCRIPT
-
Extending the Logistic Model for Mortality Forecasting and the Application of Mortality-Linked SecuritiesHong-Chih, HuangYawen, Hwang
Department of Risk Management and InsuranceNational Chengchi University, Tiapei, Taiwan, R.O.C.
-
1.IntroductionMortality risk is an important issueThe increasing demand for individual annuitiesThe improvement of mortality rate
How to construct adequate mortality modelConsidering the effects of ages and yearsThe improvement trends of different ages should be different.
How to management and hedge the mortality riskTransferring the mortality risk to the financial market by issuing mortality-linked bond
-
1.IntroductionMortality modelExtending logistic mortality model and appling this model to fit and forecast the mortality data of Taiwan, USA, and Japan
Mortality riskMortality-linked bond combining with collateral debt obligation
-
2.Literature review-mortality modelGompertz(1825) Makeham(1860) Heligman&Pollard(1980) Mortality model with 8 parameters Static model, these models only consider the effect of ages
-
2.1.Mortality modelLee-Carter(1992) Reduction Factor Model Dynamic model, these model consider the effect of age and year
-
2.1.Mortality modelWilmoth (1993)Lee and Chou (2002)Luciano and Vigna (2005)Tzeng and Yue (2005)Dahl and Moller (2006)Cairns, Blake & Dowd (2006)
-
2.2 Securitization of mortality riskBlake & Burrows (2001)derived the concept of longevity bond Swiss Re. (2003)issued the first mortality bond European investment bank (2004)issued the first longevity bond Cowley & Cummins(2005)show that securitization may increase a firms value Lin & Cox (2005)study and price the mortality bonds and swaps Cairns, Blake & Dowd(2006)show how to price mortality-linked financial instruments such as the EIB bond Blake et al. (2006)Introduce five types of longevity bonds
-
2.2 Securitization of mortality riskIn this paper, we apply the extended logistic mortality model to price the longevity model. Furthermore, we introduce the structure of collateral debt obligation to the longevity model. We hope to increase the purchasing appetence of longevity bond by complicating the concept of longevity bond.Lin & Cox (2005)
-
3.1 Logistic mortality modelsenescent death ratebackground death rateThus, this model is a dynamic model.It consider the effects of age and year. Bongaarts(2004) proposes a logistic mortality model as follows:We assume the mortality rate follows Eq(1)
-
3.1 Logistic mortality modelWe choose the MAPE (Mean Absolute Percentage Error) to measure the efficiency of fitting and forecasting.According to Lewis (1982), the standard of MAPE is described as following table:
MAPE
50%
Efficiency
Well
Good
Reasonable
Bad
-
3.2 Data and restriction Data source:1. Taiwan: the department of statistic, ministry of interior of Taiwan (http://www.moi.gov.tw/stat/index.asp )2. USA and Japan: Human mortality database (http://www.mortality.org )Restriction:Logistic model is an increasing function which is not suitable on 0-year to 1-year old. Therefore, we fit and forecast the mortality rate of single age from 30-year to 89-year from 1982 to 2000.
-
3.3 Numerical analysisThe fitting MAPE:Furthermore, we forecast the mortality data in 2001 for Taiwans female,the forecasting MAPE is 5.9883%.
Taiwan
Japan
USA
Male
Female
Male
Female
Male
Female
MAPE
5.0468
5.1428
5.1354
9.9702
3.3052
3.7506
-
3.3 Numerical analysis
Chart1
5.64065.79544.3045
5.06626.75464.4734
4.86256.47384.3841
4.9546.25664.1859
4.9616.39194.4707
5.38195.88524.3282
5.29265.71364.0285
5.32245.60553.7878
4.78975.28653.6846
5.09835.19573.3924
4.84544.91332.8471
4.52454.46082.8754
4.49624.66652.7721
4.67924.51642.5776
4.90544.05982.3686
4.61564.1151.9717
5.61633.53182.0149
5.58093.98752.1052
5.25623.96352.2272
Taiwan Male
Japan Male
USA Male
year
MAPE(%)
MAPE(year)
()
1982198319841985198619871988198919901991199219931994199519961997199819992000
alpha6.62445.64347.28255.6544.79124.72764.71295.30725.64485.66315.03595.39775.87425.59496.02486.14215.74765.96036.8523
beta9.25279.50379.02079.3579.60939.59959.59999.3589.26119.20089.39289.229.11259.22859.11088.98389.07879.01288.7729
gamma0.0701410.0718830.0628610.0692580.0824860.0831110.0978130.104550.0924890.0911520.0958670.0977190.0987490.0955120.0902430.100560.101180.0885450.073271
MAPE
300.00176360.00176360.00164980.00169460.00171780.00171780.00168650.00162810.00177850.001680.00177220.00167250.00158470.0018170.0019240.0019240.00182310.00183240.00177240.00180570.00193070.0018010.00179290.00183440.00181180.00189070.00185420.00184590.00182840.00182840.0018090.00191430.00149270.00188670.00158060.00177490.00161790.00168435.0968
310.00175370.00186640.00204220.00179170.00190720.00182050.00166620.00171980.00179530.00176620.00180040.00175720.00179570.00190140.00201130.00201010.00197880.00192040.00193960.00189180.00188390.00188390.0019650.00191710.00191810.00197680.00163570.00193190.00201920.00191660.00187890.00199960.00196980.00196980.00169620.00185880.00152570.00177145.4023
320.0017860.00197920.00180480.00189860.00192890.00193290.00181390.00182040.00185480.0018610.00185040.00185040.00202810.00199440.00214910.00210460.00181590.00201690.00215470.00198610.00191490.00197490.00195740.00200780.00194970.00207110.00181280.00202630.00215150.00201320.00214260.0020930.00191930.00206070.00218430.00195050.00158940.00186655.6578
330.00215450.00210290.00187680.0020160.00194260.00205580.00193090.00193090.00184920.00196540.00173310.0019530.00201740.00209660.00195370.00220840.0020740.00212280.00208960.00208960.00211490.00207490.00201850.00210730.0022310.00217440.00216930.00212970.00208310.0021190.00192650.0021950.00191750.00216030.0018060.00205080.00194380.00197045.675
340.00215850.00223860.00213270.00214520.00209870.00219030.00194180.00205220.00197690.00208030.00185950.00206580.00222310.00220920.00221960.00232230.00225140.00223880.00219470.0022030.00212920.00218470.00221630.00221630.00235010.00228750.00221570.00224310.00220510.00223490.00230670.00230670.00215210.00226930.00207450.00216060.0022150.00208373.1707
350.0022430.00238740.00220940.00228720.00231440.00233750.00227480.00218540.00199220.00220680.0023630.00219010.00234250.00233310.00246740.00244740.00237810.00236620.00213920.00232720.00218550.00230530.00223920.00233580.00248750.00241130.00231160.00236740.00251790.00236190.00236770.00242880.00254010.00238860.00220150.00228070.00219080.00220744.0966
360.00249150.00255050.00232510.00244330.00242970.00249850.00244460.00233150.00242940.00234590.00206820.00232680.00246940.00246940.00243470.00258470.00246590.00250580.00251510.00246350.00245690.00243770.00249330.00246680.00252370.00254690.00234960.00250380.002470.00250090.0027040.00256240.00259410.00251930.0025510.0024120.00234240.00234243.4113
370.00341660.00272940.00267340.00261490.00274140.00267470.00249010.0024920.00241040.00249910.00243640.00247720.00240040.00261940.00257260.00273540.0026740.00265890.00241630.00261280.00280770.00258310.00267840.00261040.00254930.00269550.00290140.00265320.00265310.00265310.0027530.00270850.00269660.00266230.00255580.00255580.00265240.00248974.6399
380.0029250.00292560.00299330.00280350.0030540.00286740.00267210.00266820.00263180.00266770.00262560.00264280.00273050.00278450.00252680.00290090.00295750.00282690.00294370.00277640.00258550.00274280.00292370.00276790.00300250.00285810.00318020.00281710.00265070.00281970.00287460.00286820.00281890.00281890.00299450.0027130.0027790.00265054.7245
390.00335760.00314070.00328230.00301090.00328060.00307820.00251310.00286150.00271850.00285320.0029030.0028250.00319470.00296610.00287390.00308250.0030110.0030110.00313590.00295580.00297070.00291810.00284160.00294050.0028180.00303620.00299670.00299670.00314390.00300220.00297740.0030430.0030130.00299030.00291390.0028850.00289730.0028264.5504
400.00366520.00337650.00323880.00323880.00370620.00330880.00352670.00307380.00316580.00305730.002860.00302540.00313250.0031660.0033620.00328190.00341790.0032130.00279010.00315240.00359950.00311070.00329530.00312970.00344730.00323120.00313070.00319370.00317510.00320210.00343090.0032340.00330190.00317790.00328160.00307320.00308690.00301755.7321
410.00395710.00363510.00371120.00348940.0038670.00356110.0035730.00330670.00365060.00328190.00298690.0032460.00343350.00338590.00332040.00350070.00312350.00343450.00341640.00336780.00289360.00332210.00354170.00333720.00344480.00344480.00341180.00340960.0036550.00342090.00354250.0034430.00367940.00338320.00344830.00327910.00367940.00322656.3989
420.00415150.00391850.00404720.00376470.00389890.0038370.00406630.00356240.00384140.0035290.00445360.00348860.00339180.00362780.00429850.0037410.00347930.00367730.00368440.00360390.00380630.00355430.00349470.00356450.00387960.00367860.00367770.00364620.00361010.00366040.00387160.00367150.00381230.0036080.00387470.00350420.00367260.00345456.6446
430.00457170.00422930.00410830.00406740.00445120.00413890.00428220.0038430.00417390.0038010.00436060.00375560.00491060.0038940.00373440.00400460.00409250.00394360.00378550.00386260.00374970.00380920.00395410.00381370.00400650.00393460.00406830.00390560.00418690.00392270.00407820.00392130.00421540.00385410.00388790.00375050.00402230.00370346.4892
440.00499210.004570.00490070.00440.00468670.00446890.00413310.0041510.00431680.00410020.00450750.00404930.00461020.00418690.00495240.00429390.00402130.00423550.00383730.00414610.00388830.0040890.00401440.00408680.00426440.00421480.00391410.00418990.00436980.00420990.00424930.00419450.00418410.00412330.00412770.00401990.00415890.00397495.4421
450.00494350.00494340.00529260.00476550.00519710.004830.00515860.00448890.00477520.00442930.00465450.00437240.00486450.0045090.00491330.00461140.00521850.00455560.00440540.00445670.00415760.00439620.0043460.00438610.00450750.00452170.00469440.00450160.00429620.00452420.00443120.00449320.00411580.0044180.00463930.00431450.00460030.00427115.7852
460.00555650.00535280.00574110.00516720.00571360.00522470.00508050.00485970.00542270.00479140.00504620.00472780.00537610.00486340.00553060.00495990.00557470.00490650.00566420.0047970.00426470.00473350.00450280.00471410.00503470.00485750.00504080.00484310.00493050.00486830.004730.00481980.00519170.00474050.00503840.00463670.00478410.00459437.2937
470.00645690.00580140.00600020.00560850.00615160.00565640.00563370.00526660.00581490.00518980.00563010.00511870.00562030.00525320.00559810.00534220.00504620.00529120.00597290.00516990.00603740.00510370.00510460.00507360.00486460.00522520.00528860.00521740.00518210.0052450.00501230.00517680.00453720.00509340.00508220.0049890.00533210.00494696.9014
480.00644910.0062930.00653640.00609340.00638680.00612850.00617670.0057130.00581190.00562790.00607740.00554870.00611790.00568190.00616640.00576170.00606130.00571290.00569720.00557840.00603730.00551010.00613310.00546750.00542970.00562760.00548480.00562750.005660.00565720.00563390.00556710.00527410.00547960.00509410.00537430.0055210.00533154.9492
490.00743360.00683170.00708460.00662610.00703060.00664450.00603220.00620270.00647780.00610980.00652670.00602160.00642220.00615340.00698380.0062220.00664510.0061750.00614940.00602580.00647750.0059560.00682080.0058990.00759430.00606810.00613720.00607690.00604780.00610840.00543210.00599380.0061420.00590210.00547330.00579560.00528690.00575117.0021
500.00815980.0074220.00755910.00721120.00710470.00720870.00733710.00673990.00663970.00663970.00688330.00654150.00742120.00667190.00694220.00672690.00654810.00668150.00672980.0065160.00644420.00644550.00682110.00637180.00669550.00655010.00798350.00656930.00695850.00660220.00631820.00646010.00611250.00636440.00618190.00625620.00598230.00620874.7153
510.00758660.00806880.00809490.00785390.00820480.00782540.00774680.00732920.00817940.00722250.00734560.00711330.00766660.0072420.00769210.00728080.00745180.00723660.00716340.00705280.00730490.00698260.00752450.00688980.00757590.00707760.00755010.00710870.00862290.00714240.00707940.00696970.00667490.00687010.00699010.00675980.00652680.00670785.3953
520.0087960.00877720.00855960.00855960.00849940.00849940.00796630.00797540.00751620.00786320.00830940.00774180.00815990.00786880.00859220.00788830.00811660.00784480.00805860.00764060.00801280.00757190.00733980.00745710.00807880.00765470.00795080.00769960.00800090.00773360.00881660.00752670.00704810.00742330.00668750.00731030.00719190.00725214.2644
530.00955310.00955310.00853240.00933460.0088710.0092360.00877090.0086840.00834640.00856760.00905730.00843280.00888290.00855780.00890820.00855450.00866510.00851120.00917370.00828440.0083610.00821840.00800850.00807860.00828620.00828620.00847170.00834680.00827890.00838030.00938480.00813520.00920510.00802830.00760590.0079120.00712290.00784564.6684
540.00972180.0104030.00994810.0101850.00956510.0100410.0094610.0094610.00989690.00934190.00915030.00919230.00998220.00931520.0092010.0092850.00992810.00924120.00892350.00898920.00916420.00892770.00875910.00875910.00859350.0089770.00906450.00905560.00930520.00908780.00944270.00880020.00889760.008690.0100540.00856960.00811470.00849273.8799
550.0100540.0113330.0107080.0111190.0106590.010920.0102080.0103130.0100920.0101930.0100030.0100270.00999790.0101470.0100190.0100860.00975460.0100410.00992320.00976070.0100520.00970560.0101170.00950430.00966090.00973250.00953480.00983180.0110940.00986160.00945280.00952660.00959850.00941360.00960990.00928820.00948680.00919833.2409
560.0116080.0123520.0110870.0121450.0109260.0118810.0108150.0112460.0107250.0111280.0110310.0109440.0113780.0110620.0116170.0109640.011350.0109170.0107960.0106050.0105590.0105590.0108010.010320.011040.0105590.0109670.0106820.0107080.0107080.0109830.010320.0104770.0102050.00939620.0100730.0102740.00996734.0765
570.0119080.0134670.012550.0132690.0112110.012930.0113750.012270.0115950.0121550.0116010.0119520.0120420.0120670.0119660.0119260.0128560.0118760.0123880.011530.0112490.0114940.0113030.0112130.0119920.0114620.0115390.0116120.011490.0116330.010420.0111870.0115670.011070.0110310.0109310.0108060.0108064.5693
580.0132470.0146870.012020.0145030.0131790.0140760.0121660.0133910.0123740.0132840.0123650.0130590.0121680.013170.012540.0129810.0135220.0129250.0122940.0125410.0130240.012520.0117280.0121910.0126780.012450.0121370.012630.0132940.0126450.0121540.0121330.0119280.0120150.0122880.0118680.0120030.0117195.5153
590.0154350.0160220.0157350.0158570.0139780.0153260.0132490.0146190.0143320.0145230.012420.0142740.0137470.0143820.0134990.0141370.013770.0140750.0130540.0136470.0141920.0136440.0133370.0132610.0146090.013530.0137440.0137440.0134880.013750.0130630.0131660.0127480.0130480.012730.0128920.0123770.0127144.0973
600.0157480.0174830.0178070.0173410.0159380.0166920.0138530.0159640.0143980.0158840.0145360.0156080.0151970.0157130.0140650.0154020.0149050.0153320.0148580.0148580.0165030.0148760.0151580.0144310.0152930.0147110.0154380.0149640.0146950.0149590.014510.0142940.0151390.0141770.0140090.0140090.0130370.0137995.4784
610.0176080.019080.0185660.0189680.0183550.0181810.0165060.0174370.0156710.0173780.0158370.0170730.0160770.0171740.0148990.0167890.01560.0167080.015330.0161810.0156590.0162250.0153750.0157110.0159710.0160.017030.0162970.0162850.0162790.0165210.0155250.0148690.015410.0149640.0152290.0139150.0149795.1262
620.0195070.0208250.0188220.0207510.0188770.0198070.01980.0190490.0174440.0190170.0165190.018680.0172040.0187770.0183060.0183060.0168250.0182130.0169430.0176280.0178820.0177040.0168880.0171120.0170290.0174090.0173460.0177550.0184380.0177210.0168790.0168680.0171730.0167570.0166690.0165610.0164930.0162664.4514
630.0211730.0227330.0209090.0227040.0192680.0215790.0202230.0208140.0201330.0208160.0193180.0204430.0186960.0205350.0185660.0199680.0186340.0198590.0187870.019210.0191230.0193230.0184850.0186420.0192140.0189470.0200610.019350.0194570.0192960.0179860.0183330.017850.0182270.0184050.0180140.0170110.0176664.4195
640.0255210.0248180.0241830.0248430.0225140.0235120.0218760.0227440.0231690.0227880.0221480.0223770.019840.0224630.0193310.0217850.0212530.0216580.0200340.0209380.0193940.0210950.0203930.0203160.019520.0206270.0206770.0210920.0215410.0210150.019990.0199310.0191380.0198320.0192610.0195990.0199310.019194.0827
650.0257770.0270940.0277590.0271850.0250870.0256180.0242250.0248550.0232580.0249490.024750.0244960.0243630.0245770.0230080.0237740.0217250.0236240.0201710.0228260.0215730.0230340.0209130.0221440.0214920.0224610.0207640.0229960.0229330.0228910.0216740.0216740.0219560.0215840.0208840.0213280.0199930.0208484.3408
660.0289890.0295790.0290710.0297470.0280730.0279120.027620.0271620.0273180.0273180.0242750.0268190.0256770.0268930.0256610.0259480.0244340.0257720.0230840.0248870.0231550.0251550.0233590.0241410.0224660.0244610.0235990.0250760.0219560.0249380.0225690.0235730.0240880.0234950.0233050.0232130.0226530.0226524.4325
670.0330660.032290.0315560.0325490.0293950.0304110.031060.0296830.0280620.0299120.0273720.0293620.0267050.029430.0280850.0283240.0273350.0281180.0257190.0271370.025040.0274750.0248920.0263210.0255520.0266430.025820.0273460.0242330.0271710.0254030.0256410.0241560.025580.0259080.0252680.0240030.0246145.0681
680.0359150.0352460.0373920.0356120.0331310.0331310.0340010.0324360.0332240.0327530.0321470.0321470.0303080.0322070.0299570.030920.0295460.0306780.0287580.0295920.0285760.030010.0261040.0287010.0278330.0290230.0268050.0298240.0270390.0296040.0268980.0278950.0257080.0278520.0265110.0275060.027230.0267464.5486
690.0411140.0384680.0387530.0389580.0363070.0360910.0351520.0354420.0378460.035860.0354420.0351940.0340070.0352450.0344180.0337550.0317610.0334710.0311120.0322690.0308930.032780.0293960.0312980.0296470.0316150.0300820.0325260.0296650.0322560.0279920.0303480.0286830.0303280.0278960.0299440.0281570.0290644.726
700.037370.0419780.0471420.042610.0414540.0393090.0434420.038720.0396960.0392580.0381520.0385250.0371240.0385680.0366890.0368490.0358280.0365170.0333990.0351880.035180.0358050.033630.0341290.0318250.034440.0319650.0354730.0321170.0351450.0315040.0330180.0313090.0330250.0307030.0325970.0305370.0315825.4438
710.0466370.0457990.0403020.0465950.047430.0428070.0448030.0422950.0473370.0429710.0424150.0421660.04220.04220.0412420.0402230.0417740.0398360.0390050.0383670.0376390.0391060.0356670.0372150.0352970.0375150.036560.0386850.0334540.0382890.0338250.0359220.0337860.0359610.0328880.0354850.0318780.0343156.0142
720.0504020.0499560.0508050.0509390.0425140.0466050.0523760.046190.048080.0470260.0484110.0461420.0485190.0461660.0450220.0439020.0466790.0434510.0414810.041830.0414730.0427060.039380.0405770.0389590.0408610.0402380.0421820.0396010.041710.0362090.0390790.0354710.0391550.0366180.0386250.0349460.0372825.0572
730.0514790.0544740.0534290.0556710.0550360.0507280.0482520.0504310.0572360.051450.0518940.0504810.0538580.0504930.0514680.0479090.0479170.0473860.0467220.0455970.0472560.0466290.0419530.0442360.0427060.0444990.0451090.0459880.0435880.0454290.0413730.0425090.036920.0426290.0380090.0420380.0380450.04055.488
740.0638030.0593810.0577860.060820.0576690.0551990.0573250.0550450.0517640.0562720.0609870.0552110.0583390.0552110.0587810.0522710.0576630.0516650.0520530.0496930.0518180.0509020.0490070.0482170.045820.0484530.0457910.0501270.0486930.049470.0463080.0462340.04340.0464050.0411870.0457450.0420480.0439895.9447
750.0636160.0647060.0683440.0664190.0598770.0600450.0600480.0600590.0649720.0615260.0551340.0603640.0673290.0603510.0630890.0570150.0626270.0563160.0568210.0541440.0542830.0555520.0560070.0525440.0505510.0527480.0546260.0546260.0500520.0538570.049910.0502760.0505060.0505060.0497690.0497690.0444160.0477694.3763
760.0727550.0704770.0740930.0724990.0708760.0652910.0653950.0655050.0666340.0672410.0669290.0659710.0610990.0659450.0726110.0621690.0700040.0613660.0644820.0589760.0622490.0606080.0635660.0572440.0591670.0574070.0570280.0595110.0578480.0586170.0505080.0546590.0532450.0549550.052060.0541340.0509030.0518615.1263
770.0755020.0767270.0824210.0790940.0797770.0709660.0791160.0714130.0735450.0734540.0727240.0720670.0727220.0720260.0667270.0677660.0784930.0668450.0735140.0642180.072080.06610.0663010.0623450.0644410.0624590.0659140.0648110.0639320.0637760.0580280.0594080.0565860.0597810.0573350.0588650.0579480.0562884.7515
780.0786660.0834870.086240.086240.0838120.0770980.0808410.0778150.0887640.0801980.0747440.0786850.0790830.0786290.0776320.0738340.0685170.0727820.0841390.0698980.0770470.0720590.0733050.0678760.0715790.0679310.0712680.0705540.0700730.0693630.0624840.0645480.0659620.0650080.0592520.0639880.06150.0610755.0446
790.0943510.090790.0975370.0939710.0881230.0837170.0894330.0847440.0836910.0875090.0861010.0858620.0868360.0857890.0810810.0804080.0802640.0792080.0693390.0760470.089110.0785180.0815490.0738660.0826620.0738530.0801380.0767730.0752050.0754060.0737410.0701090.0711170.0706670.0699720.0695310.0640150.0662464.297
800.0959540.0986670.105790.102320.0915310.0908530.0961240.0922330.0980190.0954250.0932770.0936350.103160.0935440.0870340.087520.0941880.0861570.0879640.0826960.077850.085510.0928730.0803470.086470.0802530.0936840.0834980.0864410.0819370.0792850.0761160.0811910.0767850.0779390.0755220.0718260.0718265.1287
810.11340.107150.109410.111330.10470.0985360.100970.100320.0975950.103980.107190.102040.107990.101930.10080.0952040.0970180.0936610.0966830.0898770.0962540.093070.0771240.0873510.102590.0871640.0919750.0907610.0984640.0889860.0831510.08260.0839480.0833930.0844080.0819910.0787350.0778424.9832
820.117650.116280.121890.121030.115550.10680.112510.109030.120170.113220.111110.111110.119650.110980.101960.103490.101750.101750.097990.0976210.101270.101230.097230.094910.0896880.0946160.105470.0985950.106480.0965840.0983250.089590.097220.0905210.0922640.0889660.0941370.0843214.2607
830.138330.126080.137820.131460.114050.115670.116730.118410.120730.123170.118740.120890.123810.120740.109130.112430.108210.110460.117710.105960.112820.110030.103060.103060.103840.102640.0968830.107030.118710.104760.109550.0971170.113620.0982010.102490.096480.096260.0912915.2376
840.12420.136580.15930.142650.1210.125170.125930.128480.135290.133860.12260.131410.12440.131230.128850.122030.122390.119830.113080.114930.128430.11950.108260.111820.109560.111270.122950.116110.099040.113550.125880.105210.119390.106460.123630.104560.11110.098787.0758
850.149560.147820.145990.154620.147510.135350.134460.139270.146890.145340.130850.142690.140630.14250.131630.132340.125380.129880.124560.124560.128760.129670.129330.121240.131440.120530.132260.125850.132180.122990.105390.11390.128440.115340.122140.113240.122680.106825.2643
860.182540.159810.186450.167410.153160.146210.1580.150830.151160.157630.150410.154790.153050.154570.147380.143390.140760.140640.137410.134880.138290.140570.132610.131340.130620.130460.137040.136290.142810.133090.146060.123210.111920.124860.140140.122550.129110.115435.5259
870.178550.172580.184560.181030.157360.15780.16650.163160.172080.170760.168360.167710.169980.167470.15520.15520.140330.152150.130270.145920.155150.152240.139480.142160.141080.141080.151520.147460.149430.14390.133180.133180.147540.135050.120180.132510.145460.124643.8847
880.177640.186160.197040.19550.169950.170120.174590.17630.174880.184750.188420.181490.181220.181220.198460.16780.164430.164430.158290.157710.156620.16470.162770.153710.157030.152430.162520.159380.184240.155430.151350.143830.151780.145940.160460.143160.128450.134484.5951
890.200540.200540.210460.210840.18290.18320.168840.190260.199610.199610.197490.196130.212420.195840.171270.181210.175970.177490.15610.170260.177970.177970.140610.166030.169580.164510.16210.172070.162240.167710.167290.155190.154160.157560.172960.154520.160780.144985.1467
MAPE5.64065.06624.86254.9544.9615.38195.29265.32244.78975.09834.84544.52454.49624.67924.90544.61565.61635.58095.2562
MAPE5.0468
()
1982198319841985198619871988198919901991199219931994199519961997199819992000
alpha1.86211.72831.65941.63661.41361.30521.28331.07611.15371.13591.05630.986861.05120.895910.933520.892180.928240.865250.76322
beta10.57510.71110.65210.65110.85210.92710.99511.16411.00810.98911.111.12110.97911.23711.15811.13411.04811.13511.21
gamma0.0330970.0292330.0382980.0381950.0390590.041550.0402750.0481030.0464830.0438930.0430140.0442870.0422680.0463110.0455020.0417730.0387910.0461410.046035
MAPE
300.000931920.000775260.000755540.000721860.00078810.00078810.000710410.000781460.000830070.000757050.000804890.000761610.000818470.000750030.000817950.00078740.00077830.00077830.000714250.000745790.000723160.000725180.000733470.000720210.000745440.000705860.000795180.000723810.000540780.000720360.00066950.00066950.000589810.000643190.000690280.00070560.000465770.000680678.8916
310.000614970.000824790.00077040.00077040.000980250.000833610.000839760.000826350.000728690.000799040.000801560.000801560.000735520.000790380.000727970.000823580.000739670.000814770.000816910.000781420.000766680.000759810.000917160.000752820.000640630.000738710.000698740.00075480.000684440.000751680.000640140.000699140.000667790.0006730.000637760.000734350.000683910.000706799.2568
320.00084480.000879840.000781730.000824420.000703590.000884230.000918380.000876270.000954580.000845840.000992890.000846120.000923160.000835410.000843280.000864020.00081130.000855480.000821180.000821180.000700260.00079850.000789270.000789270.000746940.000775370.00078850.000789480.000720520.000786680.000636310.000732270.000696390.000706290.000729660.000766490.000771960.000736027.2001
330.000852690.000941030.000782430.000884550.000832270.000940540.00093180.00093180.00093350.0008980.000745920.000895820.000873280.000885670.00100210.000909230.000970750.000900920.000765350.000865570.000841720.000841720.000750170.000829990.000785320.000816280.000809970.000828280.000948530.000825820.000714910.00076930.000767330.000743470.000822030.000802410.000768710.000768717.0617
340.00113760.0010090.000906530.000951460.000803680.00100320.000981990.000993560.000884810.000956130.00098630.000951250.000942260.000941760.000973630.000959780.00103960.000951640.000920940.00091510.000987750.000890020.000863850.000875510.000851320.000861940.000881150.000871690.000873570.000869580.000861490.000810690.000770980.000784990.000767530.000842560.00071730.000805275.6959
350.00106080.00108460.000986620.00102590.00113440.00107280.00090740.00106230.000995290.00102090.00100460.00101310.0010270.00100440.00104280.00101630.00113760.00100830.00097370.000970380.000960730.000943980.000907610.000926370.000996980.000912890.00108660.000920250.00090410.000918490.000879080.000856950.000762730.000831360.000890940.000887430.000788770.000846175.1022
360.00116860.00116860.00110420.00110880.00118690.00115030.00121930.00113870.0011160.00109310.000946550.0010820.00100820.00107420.00101560.00107950.000943390.00107150.00096560.00103210.00103620.00100430.000967410.000983210.000880530.000969750.000892830.000974590.000913110.000973170.000883080.000908660.000939910.000883140.00102420.000937580.000917330.000891925.8169
370.00160070.0012620.00130130.0012010.00120580.00123650.00111510.00122360.00113880.00117360.00116860.00115890.00115220.00115220.00115010.00115010.00109260.0011420.0011840.00110090.00103720.00107160.00116950.00104670.00103320.00103320.00103540.00103540.00106380.00103430.00101940.000966450.00108150.000940950.0010860.000993640.000973730.000943095.4208
380.00144090.00136570.00148690.00130360.00127860.00133230.00130780.00131810.00116230.00126320.00109480.00124470.00107990.00123930.00109460.00122910.00130820.00122080.00125430.00117780.0011140.00114690.0010730.00111770.00118250.0011040.00113230.00110340.00124110.00110260.00116630.0010310.00114580.00100550.00103520.00105630.000894430.00100037.8913
390.00169150.0014810.00176880.00141790.0014720.00143890.00149320.00142330.00136320.00136320.00150680.00134040.00126520.00133640.00153030.00131740.00133120.00130860.00144830.00126350.00111340.0012310.00123610.0011970.00127330.0011830.00110730.00117950.0013310.0011790.00124760.00110320.00131970.00107760.00110980.00112630.00115230.00106438.5289
400.00164880.00160910.00157590.0015450.00144740.00155750.00142580.00154020.00131670.00147450.00134080.0014470.00115720.00144480.00150480.0014160.00154570.00140670.00121940.00135920.00135010.00132490.00122020.00128570.0013630.00127120.00115770.00126460.00133260.00126440.00109580.00118390.00120830.00115810.00131060.00120460.0012120.00113597.6836
410.00169060.00175150.00190830.00168640.00175360.00168930.0017770.00167020.00184510.00159860.00134670.0015660.00131620.00156570.00143090.00152640.00150360.00151620.00134010.0014660.00126870.00142980.00156450.00138470.001380.00136950.00144420.00135980.00133090.00135990.00138490.0012740.00129130.0012480.0012920.0012920.0013020.0012167.4392
420.00191540.00190970.00207740.00184370.00182460.00183590.00190580.00181480.00179450.00173690.00179260.00169870.00147910.00170070.00164510.00164970.00162530.00163850.00151960.00158520.0017630.00154710.00148720.00149540.00176160.00147930.00147780.00146640.00157290.00146660.00134370.00137480.00153520.00134840.00140290.00138980.00154250.00130565.9425
430.00217310.00208550.0019620.00201880.00238630.00199890.00197550.00197550.00179830.0018910.00190390.00184660.00197020.00185140.00161350.00178750.00181420.00177490.00149180.00171810.00151080.0016780.00176380.0016190.00144510.00160180.00185460.00158550.00159430.00158590.00164730.00148740.00156080.00146050.00152640.0014990.0014510.00140576.9309
440.0023640.00228080.00226310.00221370.00226960.00218020.00215370.00215430.00237030.00206270.002210.00201160.00203550.00201940.00194160.00194160.00168910.00192710.00176630.00186650.00187790.00182430.00179980.00175720.00157110.00173840.00181110.00171880.00176220.00171920.00184690.00161320.00159880.00158560.00176380.00162110.00163520.00151775.491
450.00260760.00249790.00285780.00243040.00242660.00238190.00242030.00235310.00242950.0022540.00225990.00219560.0022610.0022070.00218460.00211380.00230070.0020970.00197040.00203210.00190780.00198770.00195820.00191150.00195010.00189090.00213420.0018680.00186820.00186820.00208470.00175380.0016350.00172540.00208970.00175750.00190580.0016436.5597
460.00287440.0027390.00283710.00267160.00274190.0026060.00251930.00257420.00245610.00246720.00223850.00240070.00261340.00241630.00245830.00230630.00228650.00228650.00262410.00221680.00225460.00217030.00207080.0020840.0020930.0020610.00232430.00203480.001930.00203480.00183950.0019110.00185460.00188140.0020.00190990.0017320.00178314.8005
470.00323690.00300690.00331690.00293990.00314090.00285530.0029050.002820.00273890.00270460.00262940.00262940.00281360.00264980.00273570.00252150.0025360.00249810.00275640.00242290.0030290.00237420.00238410.00227670.00227590.00225080.00214760.00222140.00249750.0022210.00210430.00208650.00203360.00205550.00223450.00208020.00209140.00193986.1477
480.00321880.00330450.00349550.00323830.00342160.00313240.00342220.00309330.00339420.00296920.00292030.00288440.00293450.00291020.00328150.00276190.00254320.00273420.00271280.00265280.00291180.00260190.00310630.0024920.00241930.00246250.00232830.002430.00231930.0024290.00254050.00228270.0023950.002250.00213710.00227050.00236230.0021157.4967
490.00363640.00363510.00371080.00357030.00363280.00344050.00319470.00339710.00326390.00326390.00335960.00316870.00335150.00320080.00319880.00303060.00312230.00299760.00310490.00290930.00294840.00285620.00324320.00273240.00332950.00269870.0025190.00266340.00280640.00266150.00239620.00250190.00258860.00246710.00245210.00248320.00231090.00231095.2778
500.00448960.00400230.00402830.00393950.00326230.00378290.00385940.00373490.0041140.00359220.00352130.00348570.00385660.0035250.00357280.00333090.00338350.00329150.00333880.00319550.00328850.00314030.0030010.0030010.00331990.00296210.00330250.00292440.00320480.00292140.0025640.00274680.002850.00270940.00274560.00272080.00245810.002536.3045
510.00439920.00441010.00448340.00435020.00416360.00416360.00425570.00411030.00403080.00395790.0037460.0038390.00415560.00388660.00365090.00366640.00361340.00361940.00399050.00351470.00353770.00345750.00321290.00330110.00357930.0032560.00345160.00321630.00366910.00321170.00322210.00302040.00288410.00297990.0030750.00298620.00310510.00277494.5443
520.00507670.00486310.00484510.00480690.00490230.00458680.00443230.00452760.0039440.00436520.0042080.00423270.00440650.004290.0040930.00404130.00426080.00398520.00412640.00387070.00344030.00381170.00399740.00363620.00357250.00358370.00345560.00354280.00368330.00353610.0035860.0033260.00316660.00328180.00316950.00328270.00320220.00304884.5966
530.00523690.00536610.0047890.00531480.0047860.00505710.0052330.00499140.00480520.00481870.00463950.00467160.00483390.00473980.00410690.00446010.00425650.00439330.00385680.00426780.0043750.00420710.00426620.00401050.0046650.00394930.00398220.00390770.00386590.00389860.00408050.00366750.00424130.00361870.00350410.0036140.00325220.00335495.6898
540.00619540.00592460.00572910.00587950.00572160.00557970.00490350.00550680.00534750.00532380.00558490.00516070.00524140.00524140.00496290.00492790.00455240.00484840.00488750.00471070.00464870.00464870.00463770.00442840.00402450.00435690.00446260.00431580.00482860.00430350.00413510.00404880.00399480.00399480.00448030.0039840.00322550.00369715.019
550.00614810.00654470.00631650.00650720.00681680.00616040.00615330.00607960.00550950.00588610.00565160.00570580.00572180.00580070.00543250.00545060.00528390.0053560.00520450.00520450.00541260.00514160.00536160.00489520.00477230.00481150.00494870.0047720.00529910.00475590.00455360.00447470.00458320.00441450.00471010.00439730.00481520.00407974.5709
560.00697460.00723310.00712350.0072050.00671130.00680560.00710810.00671590.00591790.00651220.00561050.0063130.00644920.00642430.0055960.00603420.00569570.00592210.00590930.00575510.00537740.00569180.00571620.00541620.00588480.00531830.0052180.00528190.00512990.00526120.00506420.00495040.0049540.00488270.00453110.00485880.00506540.00450735.0304
570.00754410.00799710.00714710.00798050.00745090.00752240.00703040.00742280.00716890.00720910.0068850.00698950.00632230.00711940.0063990.00668610.00607810.00655330.00579870.0063690.00636790.00630590.00609430.0059980.00606840.00588330.00626330.00585190.00561620.00582550.00560910.00548150.00540450.00540510.00549640.00537420.0050190.00498524.3217
580.00883970.00884490.00894420.00884230.00823420.00831840.00811150.00820790.00714470.00798470.00772080.0077430.0071920.00789410.00668940.00741380.00742420.0072570.00622750.00705320.00627990.00699110.00636840.00664730.00634540.00651310.00664740.00648890.00656010.00645560.00602190.00607450.00588640.0059880.00676820.00594960.00600430.00551925.0872
590.00994140.00978570.00979980.00979980.00885530.00920250.00911180.00907990.00873870.00884790.00823650.00858220.00845250.00875750.00770730.00822630.00779180.00804140.00752080.00781580.00692370.00775570.00745490.00737210.00721510.00721510.00687290.00720060.00708580.00715920.00638780.00673650.00655240.00663810.00622130.0065920.00642340.00611593.4314
600.0106070.0108290.0105740.0108630.0101810.0101840.00986340.0100480.00952530.00980810.00882920.00951660.00890830.00971950.00871740.00913320.00892520.00891560.00783860.00866570.00874990.00860870.00815860.00818080.00804790.00799740.00816640.00799580.00805310.00794470.00747550.00747550.00740370.00736310.00673590.00730920.00636240.00678253.3494
610.0106640.0119870.0117880.0120440.0115230.0112740.0102530.0111230.0102620.0108760.0106270.0105570.010090.0107910.00992490.0101450.00915320.00988980.0100130.00961250.00881930.00956010.0089520.00908310.00860380.0088690.00812620.00888410.00927860.00882140.00821820.00830020.00811450.00817160.00874430.00810950.00730010.00752714.8608
620.0137350.013270.0113770.0133560.0123080.0124830.0135720.0123160.0118560.0120640.0118140.0117150.0114480.0119840.0112180.0112740.00991540.0109750.0104070.0106670.00988750.0106210.0099780.010090.00973240.00983990.00987610.00987610.00964120.00979990.00928350.00922040.00904250.0090730.00911050.00900260.00802840.00835883.6861
630.0144280.0146930.0134880.0148110.0124320.0138250.0135570.0136390.0146880.0133850.0126870.0130030.0128120.0133130.0112540.0125340.0120280.0121840.0109950.0118420.0109420.0118040.0103450.0112120.0101310.0109210.0109660.0109840.0103170.0108910.00958150.0102470.0108760.0100780.0102060.0099990.00879690.00928745.8297
640.0160330.0162690.0153190.0164260.0146510.0153130.0138880.0151070.0148360.0148530.0141730.0144360.0150330.0147920.014080.0139380.0130620.013530.0133030.0131490.0129990.0131220.0121090.0124640.0119120.0121250.0118760.012220.0113030.0121090.0106440.0113920.0104810.0111970.0106560.011110.0108050.0103243.6626
650.0178350.0180160.0175990.0182180.0166580.0169630.0164030.0167350.01570.0164840.0160340.0160290.0156130.0164370.0157050.0155040.0156650.0150280.0141830.0146050.0139410.0145910.0134030.0138590.0129850.0134660.0126220.01360.0128620.0134670.0128550.0126690.0124870.0124450.011430.012350.0114530.0114813.2265
660.0198690.0199490.0194280.0202040.0184710.0187920.0178220.018540.018520.0182950.0174150.0178010.0177270.0182680.0177820.0172480.0168140.0166950.0155130.0162240.0149930.0162270.0152780.0154130.0141140.0149570.0149030.0151390.0146040.0149810.0140230.0140920.014350.0138340.0130770.0137310.0122890.0127733.0124
670.0216050.022090.0226570.0224050.0201850.0208190.020540.0205390.0203120.0203070.020040.019770.0196940.0203020.0194170.0191910.0191340.018550.0174020.0180260.0166370.0180490.0165550.0171440.0158340.0166170.0160230.0168560.0154950.0166680.0148040.0156780.0160230.0153820.0152710.0152710.0132950.0142133.4383
680.025350.0244590.0254940.0248440.0263740.0230640.024070.0227540.0225430.0225390.0225870.0219560.0227340.0225640.0210370.0213550.0215780.0206120.0201910.0200280.0207930.0200770.0176810.0190720.0178730.0184620.0185490.018770.0164550.0185470.017290.0174440.0165310.0171040.0159970.0169870.0164640.0158194.0733
690.0285580.0270780.0276940.0275440.027020.0255490.0270410.0252060.0273030.0250160.0255140.0243840.0246760.0250760.0248250.0237630.0224050.0229040.0217520.0222540.0221630.0223330.0211770.0212180.0188980.0205140.0200080.0209020.0194720.0206390.0188750.0194110.0186480.019020.0182510.0188970.0171270.017613.8085
700.028860.0299740.0303560.0305320.0290330.0282990.0298090.027920.028740.0277610.0281580.0270780.0291730.0278650.0288060.0264420.0258920.025450.0232120.0247260.0243070.0248410.0231550.0236050.0231520.0227930.023110.0232770.0202090.0229680.020160.0216010.0193040.0211520.0202750.0210240.0194110.0196054.3665
710.0331360.0331720.0303910.0338360.0328350.031340.0333560.030920.0329360.0308030.0336310.0300650.0309190.0309590.0308390.0294190.0309460.0282760.0277720.0274710.0268390.0276290.0263820.0262590.025190.0253240.0249560.0259220.0237660.0255590.0223230.0240370.0229060.0235210.0223420.023390.0216960.0218284.5182
720.0354150.0367020.0373830.0374880.0339210.03470.0371650.0342360.0351410.0341710.0349590.0333760.0376410.0343890.0317970.0327270.0331710.0314120.0318180.0305170.0315820.0307250.0278160.0292080.0295410.0281340.0292090.0288630.027570.028440.0245840.0267450.0245060.0261540.0262490.0260220.0242830.0243023.9796
730.0405950.0405950.0417750.041520.0389430.038410.0376860.0378990.0415910.0378980.0404940.0370420.0412840.038190.0406660.0363980.0376730.034890.0369750.0338940.0370680.0341620.0335990.0324840.0291210.0312510.0325670.0321330.031640.031640.0297930.0297550.027770.0290770.0280850.0289470.0256170.0270554.5774
740.0451230.0448870.0459170.0459680.0384380.0425040.041890.041940.0420180.0420180.0439520.0410990.0445270.0423970.0433990.0404710.0418110.0387430.040.0376350.0395440.0379730.0363580.0361180.0347370.0347060.0346280.0357670.0362140.0351940.0313970.0330980.0308090.0323220.0321950.0321950.0282380.0301163.7057
750.0513840.0496120.0505330.0508710.0481330.0470180.0459650.0463960.0470320.0465690.0461390.0455850.0506640.047050.0495190.0449840.0498220.0430070.0461070.0417770.0439890.0421970.0422920.0401470.0431090.0385320.0386650.03980.037770.0391360.0355580.0368070.0363510.035920.0343420.0358010.0318940.0335174.6984
760.0550010.054810.0573630.0562690.0555050.0519890.0495410.0513050.0521620.0515910.0503040.0505390.0522790.0521910.0549890.049980.0558970.0477240.0538340.0463580.0510620.0468720.0442990.0446110.044840.0427680.0456980.0442730.0427210.0435060.0408860.0409190.0398460.0399060.0385490.0397990.0380.0372943.964
770.0611990.0605210.0655750.0622060.0596330.0574580.0591070.0567060.0570010.0571270.0526240.0560040.0599970.0578640.0566270.0555040.0635980.0529350.0580210.051420.0592320.0520430.0538720.0495520.0492270.0474510.0513740.0492290.0486470.0483440.0454420.0454740.0410480.044320.0424560.044230.0391360.0414845.3193
780.0626060.0667890.0700520.0687270.0658790.0634680.0657560.0626420.068690.0632220.0620280.0620280.063440.0641160.0623570.0616060.0619410.0586860.0650630.0570070.0643590.0577550.0612050.0550130.0577180.0526230.0564030.0547140.0556630.0536970.0515520.0505140.0466150.0492020.0448480.0491340.0460890.0461285.1458
790.0741760.0736580.075880.075880.0695930.0700650.0691580.0691580.0711680.0699230.0714040.0686560.0674110.0709980.0635730.0683350.0683740.0650230.0627960.0631650.0732340.0640570.0654030.0610420.0661990.058330.0642420.0607760.061130.059610.059640.0560860.0545950.0545950.0524060.0545560.051270.051273.9107
800.0809790.0811760.0871090.0837130.0776960.0772940.0777160.0763020.0841520.0772810.0793950.0759410.0831780.0785620.0782320.0757460.0691570.0719980.0730150.0699450.0715580.0709990.0753610.0676910.0690070.0646190.0733320.0674680.073680.0661340.0644190.0622370.0630960.0605460.0612850.0605450.0570190.0569574.2285
810.0931570.0893910.0912830.0922760.086170.0852060.0828280.084120.0842810.0853450.0911340.0839330.0899980.086860.0872190.0838940.0771690.0796640.0774380.0773970.0807530.0786360.0725580.0750110.0803780.0715390.077310.0748440.078180.0733220.0738730.0690190.0684680.0671050.0680640.0671490.0632840.0632373.3654
820.0917730.0983520.114050.101620.0952320.0938480.0991420.0926630.0930740.094170.086040.0926870.0959480.0959480.0928360.0928360.0895540.0880720.0868820.0855750.0859180.0870220.0847520.0830580.0753310.0791420.0885510.0829590.0851620.0812290.0850890.0764840.078650.0743220.0726560.0744230.0722040.0701654.1189
830.111620.108110.116660.11180.106560.103270.0994340.101980.110790.103810.0972570.102260.106520.105880.0999680.102630.0987680.097280.0934850.0945340.0951430.0962140.094320.0918860.087370.0874820.0862080.0918730.10120.0899120.0894020.0846870.0907910.0822520.0852590.082420.0764160.0777943.7717
840.113780.118710.139010.122860.107190.113530.115610.112120.11140.114310.12020.11270.112720.116710.105240.113330.107340.107340.105830.104330.114150.106270.101840.101550.0949120.0966130.106110.101640.0933270.0994270.0983360.0936870.102880.0909490.0985320.0911980.0946020.0861815.1989
850.13140.13020.139170.134860.126140.124670.119970.123140.124090.125730.117890.124060.136360.12850.109070.1250.107490.118310.115010.115010.115370.117240.117650.112120.109430.106590.112330.112330.11150.109830.101780.103540.110580.100470.110120.100810.10370.0953844.3475
860.154050.142620.1550.147830.136480.136730.14420.135080.134270.138120.135520.136390.145420.141290.138840.137690.126560.130250.125040.126640.134760.129190.121560.123640.119110.117470.1270.123990.122390.121180.118370.11430.113480.110870.116870.111320.110180.105462.9088
870.156020.156020.170640.161810.144350.149770.143720.147990.158860.151520.134110.149750.14940.155130.144260.151450.141770.14320.123160.139270.135070.142160.136160.136160.12930.12930.13910.136680.133540.133540.126030.126030.129390.12220.131290.122780.124340.116474.0225
880.162760.170440.16910.176850.161630.163810.152920.16190.158080.165980.165720.164170.156090.170060.155360.166320.147540.15720.135910.152930.147230.156210.144520.149740.164890.142140.147090.150450.151050.146950.146360.138780.134520.134520.144980.135250.128790.128475.1678
890.197390.185890.179030.192960.17890.17890.186110.176850.168040.181520.166940.179690.180970.186120.166350.182350.172210.172310.155120.167680.171370.171370.152620.164420.146830.156020.153850.165340.16120.161460.159570.152590.14760.147880.154340.148770.160320.141515.0731
MAPE4.70175.20735.09494.32594.86235.04435.17135.37485.17446.07015.59884.59695.60444.63665.60495.09484.62694.90596.0168
MAPE5.1428
1982198319841985198619871988198919901991199219931994199519961997199819992000
alpha6.62445.64347.28255.6544.79124.72764.71295.30725.64485.66315.03595.39775.87425.59496.02486.14215.74765.96036.8523
beta9.25279.50379.02079.3579.60939.59959.59999.3589.26119.20089.39289.229.11259.22859.11088.98389.07879.01288.7729175.67550009.2460789474
gamma0.0701410.0718830.0628610.0692580.0824860.0831110.0978130.104550.0924890.0911520.0958670.0977190.0987490.0955120.0902430.100560.101180.0885450.073271
alpha1.86211.72831.65941.63661.41361.30521.28331.07611.15371.13591.05630.986861.05120.895910.933520.892180.928240.865250.76322
beta10.57510.71110.65210.65110.85210.92710.99511.16411.00810.98911.111.12110.97911.23711.15811.13411.04811.13511.21208.646000010.9813684211
gamma0.0330970.0292330.0382980.0381950.0390590.041550.0402750.0481030.0464830.0438930.0430140.0442870.0422680.0463110.0455020.0417730.0387910.0461410.046035
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
male
female
year
10^(-5)
alpha
MAPE
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
male
female
year
10^(-2)
beta
beta
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
male
female
year
10^(-2)
gamma
()
1982198319841985198619871988198919901991199219931994199519961997199819992000
MAPE5.64065.06624.86254.9544.9615.38195.29265.32244.78975.09834.84544.52454.49624.67924.90544.61565.61635.58095.2562
MAPE4.70175.20735.09494.32594.86235.04435.17135.37485.17446.07015.59884.59695.60444.63665.60495.09484.62694.90596.0168
MAPEMAPE
305.09688.8916
315.40239.2568
325.65787.2001
335.6757.0617
343.17075.6959
354.09665.1022
363.41135.8169
374.63995.4208
384.72457.8913
394.55048.5289
405.73217.6836
416.39897.4392
426.64465.9425
436.48926.9309
445.44215.491
455.78526.5597
467.29374.8005
476.90146.1477
484.94927.4967
497.00215.2778
504.71536.3045
515.39534.5443
524.26444.5966
534.66845.6898
543.87995.019
553.24094.5709
564.07655.0304
574.56934.3217
585.51535.0872
594.09733.4314
605.47843.3494
615.12624.8608
624.45143.6861
634.41955.8297
644.08273.6626
654.34083.2265
664.43253.0124
675.06813.4383
684.54864.0733
694.7263.8085
705.44384.3665
716.01424.5182
725.05723.9796
735.4884.5774
745.94473.7057
754.37634.6984
765.12633.964
774.75155.3193
785.04465.1458
794.2973.9107
805.12874.2285
814.98323.3654
824.26074.1189
835.23763.7717
847.07585.1989
855.26434.3475
865.52592.9088
873.88474.0225
884.59515.1678
895.14675.0731
()
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
male
female
year
MAPE
MAPE(year)
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
male
female
age
MAPE(%)
MAPE(age)
(year)
1.38551.42761.31941.30781.29481.25861.29761.21231.18031.14081.14841.09081.04991.06531.06170.996740.97550.956380.91184
0.0529960.0360880.049770.0446380.0437170.0422980.0398170.0445590.0445830.0438190.0413620.0423080.0422970.0416230.0402430.0400040.0374340.0432490.042705
6.65046.82896.21646.15016.2386.05316.12245.77215.71575.4635.59695.28135.32095.53335.47185.12545.05735.06434.8787
0.0697720.0551670.0816070.0629970.0653010.0679310.0724780.0998060.0911060.0980610.089790.099310.110740.0963660.0981440.115570.112420.105280.1085
(year)
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
(age)
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Japan Male
total0123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100
9010963917118043146342135136128292154971154853156362154829157281153016151838159745149190164133148688145423163680175771181675191628197011195525199883194536186558202872175781173128172714174154179454184741185816185302176880190914188676191654194914192064189700187791187007181107172623178191173748165273159304155783158807133458124482109550968187901271497834218544084362852468580182341768207609671290704796729962812606085954956443530524992646058439203920435254317053044428175230641931416958153261215010795949679956673499638062877200314951083788507346230646
479846967458483027413117151925193323445662928181846688937188647886100971311291361501481841932242322142592842773063503253303813733993813593313354184364955335716416547087468248619029541008115112001202131413401392128413831409154115351430133513141324116212471140111993780664150542232125618012610668125
Japan Female
T123456789101112131415161718192021222324252627282930
payment0000000000000009.563520.72433.66948.59165.69285.176107.25192.47272.91348.35418.62483.57543.09597.12645.67
indexindex*1.1realindex*1.4
10.99321.092520.99461.3904800
20.985941.0845340.988971.38031600
30.978171.0759870.983091.36943800
40.969831.0668130.9771.35776200
50.960871.0569570.970711.34521800
60.951231.0463530.964241.33172200
70.940841.0349240.957611.31717600
80.929631.0225930.950861.30148200
90.917531.0092830.944011.28454200
100.904450.9948950.93711.2662300
110.890310.9793410.930161.24643400
120.875030.9625330.923231.22504200
130.858520.9443720.916341.20192800
140.840680.9247480.909541.17695200
150.821440.9035840.902861.15001600
160.80070.880770.896331.120980.01556155599.9999999991.56E+05
170.778380.8562180.889991.0897320.033772337719.9999999993.38E+05
180.754430.8298730.883871.0562020.0539975399705.40E+05
190.728770.8016470.877991.0202780.076343763429.9999999997.63E+05
200.701380.7715180.872390.9819320.10087210087201.01E+06
210.672230.7394530.867070.9411220.12761712761701.28E+06
220.641340.7054740.862050.8978760.15657615657601.57E+06
230.608750.6696250.857360.852250.18773518773502.44E+06
240.574560.6320160.852980.8043840.22982422982402.30E+06
250.538890.5927790.848930.7544460.21555621555602.16E+06
260.501920.5521120.845210.7026880.20076820076802.01E+06
270.46390.510290.84180.649460.1855618556001.86E+06
280.425130.4676430.83870.5951820.17005217005201.70E+06
290.385950.4245450.83590.540330.1543815438001.54E+06
300.346770.3814470.833370.4854780.13870813870801.39E+06
USA Male
Year1982198319841985198619871988198919901991199219931994199519961997199819992000Total
Taiwan MaleMAPE5.64065.06624.86254.9544.9615.38195.29265.32244.78975.09834.84544.52454.49624.67924.90544.61565.61635.58095.25625.0468
Taiwan FemaleMAPE4.70175.20735.09494.32594.86235.04435.17135.37485.17446.07015.59884.59695.60444.63665.60495.09484.62694.90596.01685.1428
Japan MaleMAPE5.79546.75466.47386.25666.39195.88525.71365.60555.28655.19574.91334.46084.66654.51644.05984.1153.53183.98753.96355.1354
Japan FemaleMAPE8.03529.00629.46279.471610.6110.46210.74710.6810.06810.31710.2489.90269.825910.0669.836210.12210.11410.04110.4179.9702
USA MaleMAPE4.30454.47344.38414.18594.47074.32824.02853.78783.68463.39242.84712.87542.77212.57762.36861.97172.01492.10522.22723.3052
USA FemaleMAPE4.18944.54383.94994.69584.15494.41394.39894.12614.06563.99643.45233.47773.09663.12762.84182.90593.10213.32953.39273.7506
USA Male
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Japan Male
Japan Female
year
MAPE(%)
MAPE(year)
USA Female
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
USA Male
USA Female
year
MAPE(%)
MAPE(year)
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
Taiwan Male
Japan Male
USA Male
year
MAPE(%)
MAPE(year)
Taiwan MaleTaiwan FemaleJapan MaleJapan FemaleUSA MaleUSA Female
MAPEMAPEMAPEMAPEMAPEMAPE
305.09688.89166.999711.4159.26045.0556
315.40239.25684.44898.88546.91054.2045
325.65787.20012.99479.48926.51282.615
335.6757.06172.67616.68715.6471.987
343.17075.69593.72915.20281.45481.524
354.09665.10222.96242.93242.31242.21
363.41135.81694.06774.3771.34922.6344
374.63995.42083.80356.56732.1274.4896
384.72457.89133.50054.14513.34723.7433
394.55048.52894.74554.81845.91586.4027
405.73217.68364.18336.99255.66914.1912
416.39897.43923.44318.25816.25534.4148
426.64465.94252.961510.325.17892.6516
436.48926.93093.3411.9286.51513.8022
445.44215.4914.145412.6068.32824.3063
455.78526.55974.683212.3586.6083.5936
467.29374.80055.18612.7035.57352.1335
476.90146.14775.785913.2365.26741.8193
484.94927.49675.855813.672.88193.6154
497.00215.27787.184214.4267.04752.5885
504.71536.30457.058213.4544.81742.7503
515.39534.54437.553612.3432.63224.2608
524.26444.59667.669610.3812.05734.7597
534.66845.68986.71598.20471.87394.0631
543.87995.0195.73255.62312.40652.477
553.24094.57096.03314.77932.35172.6688
564.07655.03044.70672.11952.3343.3052
574.56934.32174.04662.2891.55222.4331
585.51535.08724.45343.5745.54415.9209
594.09733.43144.15824.792.24312.4003
605.47843.34944.38396.26744.3642.8552
615.12624.86084.91767.73064.55644.1062
624.45143.68615.41518.99776.34375.0385
634.41955.82975.413410.1854.20542.9669
644.08273.66266.438311.3082.71981.2225
654.34083.22657.210512.5363.26411.392
664.43253.01247.371612.7562.46661.6468
675.06813.43838.129813.721.86212.36
684.54864.07338.576113.173.16791.7413
694.7263.80858.763412.9511.79663.8936
705.44384.36659.037412.7041.97733.5889
716.01424.51829.174611.0751.56723.6962
725.05723.97968.377810.4491.92192.1715
735.4884.57747.52788.3161.81342.6029
745.94473.70576.30825.98191.36955.0286
754.37634.69845.73853.64011.50155.0468
765.12633.9644.55011.39871.48594.2835
774.75155.31933.57611.91.71954.6291
785.04465.14582.06613.4071.90464.4201
794.2973.91071.50886.61522.20343.5364
805.12874.22851.55528.89511.59632.3201
814.98323.36542.11311.4271.14461.4164
824.26074.11893.32213.7741.2011.4175
835.23763.77173.581915.5641.34682.9294
847.07585.19894.100417.4021.12514.2664
855.26434.34754.339618.9221.22155.6186
865.52592.90884.771920.4561.11827.387
873.88474.02254.962421.8081.23438.9049
884.59515.16785.117922.7361.78859.8127
895.14675.07314.951923.5432.35311.712
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Japan Male
Japan Female
age
MAPE(%)
MAPE(age)
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
USA Male
USA Female
age
MAPE(%)
MAPE(age)
1982198319841985198619871988198919901991199219931994199519961997199819992000
alpha2.30252.85123.18072.57242.80262.25772.16252.10972.12482.19972.34282.33322.19412.13822.16782.08692.19112.08552.1568
beta10.43210.1719.973410.23310.07510.32110.39910.37310.38210.3210.21710.19810.22610.2810.17910.20910.13210.18810.07
gamma0.0356060.0282980.0186910.0256210.0169380.0256730.0237310.0234650.0229350.0191140.0168130.0140570.0189470.0205710.022640.0235950.0273810.0319890.03019
MAPE
300.000940.000882190.001030.000885530.000820.000820290.000810.000810.000810.000744720.000810.000755770.000740.000726610.000780.000708330.00080.00070770.000760.000677190.000770.000670090.000720.000637620.000740.000660860.000810.000672650.00070.000685570.00070.000682070.000750.000731460.00080.000762830.000750.000744126.9997
310.000940.000940.000950.000950.000960.000886670.000770.000869630.000760.000805660.000810.000810.000770.00078020.000790.000760070.000760.000760.000730.000730.000770.000724050.000730.000690950.00080.000711590.000760.000723190.000810.000734740.000730.000730.000840.000780230.000820.00081030.000860.000790954.4489
320.000970.00100420.0010.00102140.000960.000960.000920.000935680.000840.000873060.000850.000870120.000850.000839660.000850.000817470.000830.000818020.000820.000788540.000810.000783820.000750.000750.00080.000767770.000830.000779180.000820.000789180.000840.000783070.000820.00083420.00090.000862870.000870.000842732.9947
330.001050.00107540.001050.00110040.001030.0010410.001010.00100880.001030.000947580.000970.000936760.000860.000905620.000830.000881130.000890.000882370.000820.000853440.000850.000850.000810.000815380.000830.000830.000810.000841240.000850.000849440.000820.000841850.000930.000893920.000890.000921070.00090.00092.6761
340.001120.00115440.001120.00118780.001050.00113050.001070.00108990.001030.001030.000980.00101060.000960.000978810.000880.000951740.00090.000953760.000930.000925390.000860.000923290.000930.000887780.000850.000898920.000910.000910.000830.000916150.000920.000906930.000960.000960.000980.00098550.000940.000963323.7291
350.001190.00124210.001220.00128460.001240.00122940.001180.00117960.001120.00112110.001030.00109250.001060.001060.0010.00103010.000990.00103290.000930.00100510.000940.00100450.000930.000967930.000980.000975240.000990.00098620.000990.000990.000920.0009790.000990.00103310.001070.00105680.001030.00103332.9624
360.00120.00133940.001380.00139170.001310.00133860.001270.0012790.001210.00122190.001140.00118330.001120.00115010.001060.00111690.001070.00112080.001120.00109360.001010.00109430.001080.00105670.001050.00105980.001050.00107060.001060.00107170.000980.00105880.001090.0011140.001070.00113580.0010.00111084.0677
370.001410.00144740.001270.00151020.001460.00145920.001350.00138910.001340.00133330.001260.0012840.001250.001250.001130.00121320.00120.00121820.001150.00119160.001150.00119390.001140.00115490.001060.00115340.001130.00116420.00110.00116220.001160.00114720.001210.00120350.001160.00122320.001160.00119643.8035
380.001640.00156730.001650.00164150.001480.00159240.001530.0015110.001450.00145660.001380.00139550.001370.00136090.001230.00132010.001250.00132630.001230.00130020.001280.00130410.001230.00126370.001150.00125710.001230.00126790.001180.00126240.001180.0012450.001290.00130260.001320.001320.001280.00129113.5005
390.001710.00170030.001930.00178670.00170.00173960.001450.0016460.001660.00159280.001570.00151920.001470.00148380.001440.00143860.00140.00144610.001330.00142060.001340.00142610.001370.00138410.001290.00137190.001240.00138270.001370.00137330.001240.00135330.00130.00141210.00140.00142710.001360.00139584.7455
400.00210.00184780.002040.00194740.002060.00190220.001870.00179550.001660.00174340.001780.00165620.001580.00162020.001570.001570.001580.00157910.001510.00155410.001540.00156130.001510.00151750.001450.0014990.001510.001510.001370.0014960.001350.00147330.001490.00153340.00150.00154570.001450.00151154.1833
410.002050.00201160.002190.00212530.002110.00208170.002080.00196110.001910.001910.001690.00180820.001870.00177160.001690.00171570.001710.00172650.001650.0017020.001650.00171090.001570.00166510.001620.00163980.001560.0016510.001560.00163190.001490.00160610.001660.00166750.001620.0016770.00160.00163953.4431
420.002380.00219330.002440.00232220.002390.002280.002130.00214450.002230.00209410.001990.00197650.001870.00193940.002010.00187740.001890.001890.001850.0018660.001890.00187660.001790.00182840.001780.00179570.001760.00180730.001720.00178220.00170.00175320.001750.00181590.001780.00182240.00180.0017812.9615
430.002330.00239490.002540.002540.002580.00249910.002450.00234750.002320.00229770.002310.00216320.002260.00212560.001990.00205660.002190.00207130.002150.00204770.002060.002060.002040.00200930.001890.00196840.001950.00198040.00190.00194860.001840.0019160.001910.001980.001980.00198320.001780.00193743.34
440.002860.00261850.002810.0027810.002840.00274090.002720.00257230.002670.00252280.002370.002370.002510.00233210.002360.00225530.002020.00227240.002480.00224910.002290.00226310.002280.00220950.002260.00215950.002160.00217210.002130.00213280.002030.00209620.00220.00216160.002260.00216130.002170.00211044.1454
450.003240.00286670.003240.00304780.003060.0030080.002830.00282120.0030.00277160.002840.00259920.002670.00256110.002820.00247570.00250.00249540.002320.00247240.002660.00248790.002560.00243110.002460.00237120.00250.00238460.002420.00233670.002320.00229580.002380.00236250.002420.00235840.002370.00230164.6832
460.003710.0031420.003490.00334290.003390.0033030.003190.00309680.00320.00304660.002980.00285320.003020.00281510.002720.002720.002980.00274270.00280.00271970.002480.00273680.003030.00267640.002750.00260550.002730.00261990.002650.00256220.002580.00251670.002670.00258470.002750.00257650.002520.0025135.186
470.004050.00344730.00410.00366940.00380.00362870.003830.00340190.003430.00335060.003260.00313470.003250.00309680.003150.00299090.003050.00301690.003270.00299380.00310.00301230.002860.00294790.003080.0028650.003140.00288060.002920.00281190.00290.00276120.002960.00283040.002980.00281790.002860.00274675.7859
480.004510.0037860.004450.00403060.004150.00398830.003960.00373970.003910.00368670.003410.00344660.00350.00340920.003420.00329120.00350.00332090.003390.00329760.003570.00331730.003330.00324840.002990.00315220.003540.00316940.003310.00308810.003170.00303190.003340.00310230.003290.0030850.003180.0030055.8558
490.005030.00416170.004980.00443020.004690.00438530.004620.00411360.004280.0040580.004140.00379220.003630.00375550.003680.00362420.003780.0036580.003770.00363410.003760.00365490.003870.00358090.003670.00347010.00320.00348920.003780.00339380.003610.00333140.003690.00340290.00370.00338070.003510.00329067.1842
500.005490.00457840.005620.00487220.005380.00482350.004930.00452750.004850.00446840.004330.00417510.004510.00413960.004020.00399330.004080.00403160.004130.00400690.004130.00402860.00410.00394880.004190.00382210.003950.00384340.003710.00373190.004150.0036630.004220.00373550.004180.00370780.003940.00360627.0582
510.005840.00504050.006140.0053610.006020.00530730.00570.00498550.005530.0049220.005110.00459930.004740.00456540.004760.00440240.004190.00444590.004420.004420.004510.00444210.004530.00435590.004290.00421160.004830.00423570.004360.00410610.004030.004030.004620.00410320.004520.00406980.00430.0039557.5536
520.006320.00555290.006710.00590170.006460.00584130.006470.00549240.006120.00542310.005660.00506910.005440.00503740.00520.00485580.005150.0049050.004730.00487760.004890.00489960.004970.00480640.005010.00464280.004770.00467010.00490.004520.004830.00443610.00450.00450980.005140.00447030.004880.00434047.6696
530.006860.0061210.006810.00649950.007010.00643060.006760.00605330.006760.00597670.006370.00558960.006210.00556060.005780.00535830.005520.00541380.005440.00538440.005140.00540590.005270.00530470.005170.00511990.005470.00515110.005210.00497790.005390.00488550.005370.00495930.004930.00491340.005580.00476646.7159
540.007090.00675080.007570.00716050.007550.00708090.007430.0066740.007380.00658830.007180.00616590.006840.00614050.006370.00591510.006230.00597770.006090.00594570.006030.00596610.005680.0058560.005660.00564790.005730.00568360.005680.00548430.005610.00538260.006120.00545640.005930.00540350.005170.0052375.7325
550.007870.00744890.008130.00789130.008130.00779840.007770.00736060.007810.00726390.00790.00680420.007650.00678320.007340.00653210.007060.00660260.006910.00656730.006680.00658580.006730.00646570.005950.0062320.006450.00627320.006230.00604440.006260.00593270.006060.00600580.006810.00594560.006240.00575716.0331
560.008480.00822260.008790.00869910.008590.008590.008850.00812010.008240.00800990.008340.00751090.008280.00749530.008050.00721560.008040.00729490.007460.00725550.007590.00727120.007140.007140.007020.00687830.006730.00692570.006820.00666380.006750.00654120.00690.00661310.006750.00654520.00710.00633154.7067
570.009080.009080.009320.00959180.009130.00946310.008960.008960.009190.00883380.00890.00829320.009280.00828430.008870.00797270.008760.00806180.00830.00801750.008320.00802930.008340.00788560.007560.00759320.007810.00764790.006850.00734860.007190.00721420.007460.00728440.007560.00720820.007060.00696614.0466
580.009610.010030.010060.0105780.009930.0104260.009530.00988880.009430.00974340.009670.00915920.009560.00915830.009670.00881120.009560.00891120.00970.00886090.009190.00886760.009040.008710.008630.00838380.008380.0084470.008270.00810570.007420.00795840.008080.00802610.008150.00794130.008150.00766694.4534
590.010590.0110820.010830.0116680.010530.0114880.010580.0109160.010430.0107480.010150.0101180.010490.0101260.010210.00973970.010290.00985190.010380.00979430.010590.00979440.010050.00962130.009460.00925810.009690.00933120.008690.00894260.009110.00878140.008350.00884570.008880.00875180.008570.00844094.1582
600.011480.0122470.011440.0128710.011590.0126580.011310.0120510.011190.0118560.011090.0111780.011050.0111980.011180.0107680.011350.0108930.011390.0108270.011360.0108190.011230.0106280.010750.0102250.010550.0103090.010070.00986750.009580.00969120.00980.0097510.009170.00964760.009430.00929544.3839
610.012450.0135380.012510.0142010.012490.0139480.01240.0133050.011870.0130780.0120.0123510.0120.0123850.011730.0119060.012440.0120460.012110.011970.012360.0119510.012310.0117410.012050.0112930.01180.0113910.011390.0108890.010810.0106970.010730.0107510.010590.0106380.009630.0102394.9176
620.013860.0149660.01370.0156680.013450.0153690.012980.0146910.013010.0144270.012780.0136480.013440.0136980.012720.0131650.013120.0133220.013340.0132340.013290.0132020.013790.0129710.013160.0124740.013320.0125870.012680.0120190.012160.0118080.011840.0118550.011490.0117320.011280.011285.4151
630.015540.0165460.015270.0172870.014520.0169350.01440.0162210.013940.0159150.014170.0150830.014190.0151510.014110.0145580.014280.0147330.014250.0146310.014710.0145840.014420.0143290.014520.0137790.014330.0139090.014020.0132660.013170.0130360.013050.0130740.012940.012940.012260.0124295.4134
640.016660.0182940.016440.0190730.016790.0186590.015510.0179110.015330.0175550.015290.0166680.015110.0167580.015210.0160980.015450.0162950.015220.0161760.01570.016110.016260.0158280.015220.015220.015760.0153710.015240.0146430.014960.0143930.014420.014420.014090.0142750.013850.0136976.4383
650.018460.0202280.018060.0210430.017810.0205570.017790.0197760.016670.0193620.016620.018420.016210.0185360.016570.0178020.016460.0180210.016640.0178820.016890.0177950.017160.0174830.017120.0168110.016690.0169850.016720.0161630.016020.015890.016220.0159050.015780.0157480.014870.0150957.2105
660.020780.0223640.02040.0232150.019720.0226450.018940.0218340.01930.0213530.017870.0203550.017930.02050.017810.0196840.018420.0199290.0180.0197680.018650.0196540.018220.0193090.017980.0185680.018930.0187680.017840.017840.017880.0175440.017620.0175430.017770.0173740.016460.0166367.3716
670.023120.0247250.022570.0256080.02170.0249420.020940.0241030.020810.0235460.019980.0224920.019810.0226710.019580.0217650.01940.0220370.01960.021850.020020.0217050.020250.0213240.019350.0205070.019770.0207370.019780.0196910.019050.0193690.019220.0193490.019140.0191690.018320.0183368.1298
680.025540.0273320.024890.0282440.024150.0274680.023510.0266050.022740.025960.021850.024850.022670.0250680.021670.0240620.021540.0243650.021760.0241480.022080.0239660.022170.0235450.021410.0226450.021460.0229090.02060.0217310.021140.0213820.020720.021340.020690.0211480.019650.0202088.5761
690.027750.030210.02740.0311450.026380.0302430.027150.0293620.025150.0286160.024290.0274510.02440.0277150.024480.0265970.023530.0269350.023850.0266840.023970.0264590.023940.0259920.023220.0250030.023880.0253060.022940.0239810.022640.0236020.023240.0235340.022730.0233310.022160.0222718.7634
700.031280.0333840.030840.0343370.029460.0332910.028780.0323970.02810.0315370.027240.0303180.027290.0306350.026150.0293950.026770.029770.025840.0294790.026330.0292050.026150.0286890.025490.0276020.026520.0279480.025540.0264590.024390.0260480.02490.0259510.025180.0257360.023720.0245429.0374
710.035640.0368830.034590.0378460.033010.0366360.031770.0357370.03120.0347470.030250.0334780.030390.0338540.029360.0324790.029070.0328970.029280.032560.028480.0322280.028790.0316570.027710.0304640.028810.0308590.02710.0291880.027160.0287440.026880.0286110.026670.0283850.026270.0270429.1746
720.039030.0407370.038780.0417020.036730.0403050.035920.0394110.034810.0382720.032810.0369580.034120.0374010.033450.0358780.032820.0363410.031790.0359530.032580.0355550.031280.0349230.031060.0336150.031550.0340660.030180.0321920.030290.0317110.029690.0315380.029960.0313020.028240.0297918.3778
730.043910.0449780.043030.0459340.041220.0443270.041330.0434470.03830.0421410.037170.0407860.037940.0413060.036240.039620.036770.0401340.036070.0396870.035520.0392130.035980.0385140.033790.0370810.034530.0375950.033340.0354970.032550.0349770.032810.0347570.033290.0345110.031410.0328147.5278
740.048940.0496430.04970.0505760.047310.0487320.046010.047880.043290.0463850.041140.0449960.042340.0456020.040840.0437380.041030.0443070.039760.0437940.039820.0432320.038830.0424590.038660.0408910.038930.0414760.036980.0391290.035390.0385680.035820.0382940.036270.0380390.034970.0361356.3082
750.055390.0547670.054680.0556620.052070.0535510.051140.0527420.048830.0510340.046580.049620.047130.0503250.04510.0482640.045310.0488950.044470.0483060.044290.0476450.043650.046790.041770.0450770.044180.0457420.040080.0431180.039940.0425140.038910.0421790.040.0419160.037770.0397815.7385
760.060010.060390.061230.061230.058820.058820.058070.058070.05410.0561240.05230.0546940.052310.055510.049880.0532360.051130.0539330.049660.0532580.04940.0524850.049590.0515410.046870.0496710.047170.0504240.045380.0474970.043850.0468470.043210.0464410.043620.0461730.042080.0437824.5501
770.068410.0665540.066080.0673180.066430.0645730.06550.0639030.060720.061690.058870.0602580.059420.0611980.056730.058690.055870.059460.055430.058690.05530.0577880.054630.0567470.052340.0547080.053690.0555610.049660.0522980.05150.0515990.048730.0511130.04890.0508420.046020.0481683.5761
780.074590.0733020.074980.0739660.070440.0708490.072490.0702810.067770.067770.066350.066350.067430.067430.064520.0646670.063510.0655170.061310.0646390.061190.0635940.060890.0624460.059640.0602260.059610.0611890.057110.0575570.053850.0568080.054780.0562310.055290.0559580.051190.0529722.0661
790.083280.0806780.082610.0812170.080680.0776850.077210.0772450.076530.0744040.073160.0730130.07480.0742480.071210.071210.072610.0721450.069790.0711480.06840.069940.068230.0686760.065620.0662630.0670.0673480.062150.0633130.062510.062510.059160.0618310.061560.061560.056530.0582291.5088
800.091280.0887290.091130.0891130.088250.0851230.088690.0848390.082980.0816310.084030.080290.082970.0816980.078710.0783620.079390.079390.078260.078260.076870.076870.075480.075480.072860.072860.072980.0740810.069320.0696030.068650.0687450.066370.067950.066570.0676850.065610.0639761.5552
810.100780.0975020.102350.0976970.098980.0932020.095750.0931060.09380.0894940.088770.0882260.095160.0898260.087940.0861670.088830.0872960.086150.0860180.085870.0844260.084030.0828990.079370.080060.081430.081430.076470.076470.077030.0755540.074630.074630.076860.0743750.070250.070252.113
820.112260.107040.112560.107010.108070.101960.107690.102090.102390.0980360.099640.0968670.100910.0986770.101620.0946720.09820.095910.096080.0944690.094540.0926510.095480.0909770.089750.0879050.091750.089440.082970.0839550.08220.082980.083330.0819110.08450.0816710.080410.0770923.322
830.118280.11740.124440.117110.121110.111450.115880.111840.113330.10730.109270.106260.113390.10830.105450.103920.111890.105280.106020.103660.105730.101590.105360.0997580.100830.096440.102780.0981550.092640.0921020.092250.0910660.089870.0898370.093840.0896160.087440.0845423.5819
840.13410.128620.13240.128020.133170.12170.129770.122390.123670.117320.119850.116440.123040.118740.117530.113970.117780.115450.121630.113630.116870.111290.112570.109290.110540.105710.113310.107620.103910.100950.102130.0998570.099110.0984490.102640.0982550.098620.0926434.1004
850.140890.140740.147880.139780.140190.132760.142540.13380.137350.128150.131360.127470.136730.130040.130580.124850.134010.126460.127610.124430.131260.121790.126560.11960.121950.115760.12360.117880.115670.110560.113450.10940.109950.107790.111930.107630.103670.101444.3396
860.155570.153810.155950.152450.156450.144650.149440.146090.149090.139820.144810.139370.149460.142240.146050.136610.144040.138360.141820.13610.142070.133130.143420.130750.135720.126630.137810.128980.127420.120950.124720.119730.120740.117910.122860.117790.116180.110974.7719
870.165780.167860.173160.166040.164920.157420.168050.15930.158890.152370.159750.15220.166120.155390.155380.14930.159120.151190.154890.148680.154150.145360.148420.142780.15230.138360.150950.140960.139520.132180.13840.130890.134250.128840.138240.128770.12650.121274.9624
880.182910.182910.18690.180590.183370.171090.179810.173470.177010.165830.167370.165980.180460.169510.169740.162940.172880.164980.170210.162210.168780.15850.169160.155710.158860.1510.171220.153860.150230.144280.150990.142930.148040.140620.1520.140610.141190.13245.1179
890.199070.198990.201910.196110.195740.185690.195170.188620.188610.180230.189480.180750.19240.184640.189340.177570.189070.179770.185470.176710.18420.17260.180470.169580.172550.164560.176590.167710.171140.157290.164780.155880.160980.15330.164210.153350.155050.144374.9519
MAPE5.79546.75466.47386.25666.39195.88525.71365.60555.28655.19574.91334.46084.66654.51644.05984.1153.53183.98753.9635
MAPE5.1354
1982198319841985198619871988198919901991199219931994199519961997199819992000
alpha0.464760.471860.450510.423110.605680.744160.77950.92920.688130.795420.726830.625920.642810.615440.613030.705850.957990.714210.89285
beta11.87311.81911.81311.87311.27510.93110.87710.52910.92210.70210.81211.03510.88910.97210.8710.64810.17110.59810.169
gamma0.0446820.0469190.0408660.0396280.0350740.0262830.0249240.0216780.0283130.0222810.0237310.0252320.0252090.0273790.0268730.0256480.0221850.0259190.02291
MAPE
300.000520.000610520.000510.000632710.000470.000564530.00050.000545310.000440.000529030.000430.000460390.000410.000452890.000410.000435490.000420.000465370.000420.000420.000380.000423560.00040.000423790.000380.000420620.000410.000439210.000350.000428560.000380.000428670.00040.000424340.000390.000430820.00040.0004177211.415
310.000570.000631150.000520.000653220.000560.000584070.000480.000564090.000460.00055030.000430.00048320.000460.000476290.000430.000459770.000450.000486390.000420.000442270.000430.000444820.00040.000443790.000440.000440.000420.000458390.000420.000446910.000410.000448010.000410.000446010.000450.000450.000410.000437918.8854
320.000590.000654380.000530.00067630.000530.000606060.000540.000585240.000520.000574110.000470.000508650.000460.000502370.000430.000486740.000440.000509850.000440.000467050.00040.000468510.00040.000466120.000460.000461610.000480.000479790.000470.000467370.000480.000469530.000470.000470.000430.000471330.000420.000460259.4892
330.000640.000680540.000590.000702280.00060.000630810.000570.000609060.000520.000600760.00050.000537040.000520.000531450.000510.000516710.000490.000536010.000470.000494630.000480.00049490.000510.000491060.000450.000485710.000480.000503670.000490.000490170.000460.000493460.000490.000496560.000440.000495040.000450.000484996.6871
340.000710.000710.000720.000731520.000640.000658660.000630.000635880.000570.000630590.000570.00056870.000540.000563860.000550.000550.000520.000565180.00050.000525330.000470.000524310.000490.000518910.000490.000512570.000560.000530320.000480.000515590.000470.000520080.000480.000525960.000560.00052140.00050.000512375.2028
350.000770.000743170.000770.000764420.000690.000690.000640.000666070.000630.000663980.000580.000604020.00060.00060.000550.000586990.00060.000597720.000570.000559490.000580.000557070.000550.000550.000520.000542530.000540.000560060.000520.000543930.000570.000549690.000580.000558510.000540.000550710.000560.000542682.9324
360.00070.000780510.000830.000801440.000780.000725270.000730.000700070.000720.000701350.000640.000643410.000640.000640290.000640.000628080.000620.000634020.000590.000597510.000590.000593570.000580.000584720.000580.000575930.000540.000593240.000520.000575520.000550.000582620.00060.000594530.000550.000583290.000510.000576234.377
370.000820.000822570.000730.000843110.00090.000764950.00080.000738360.000780.000743180.00070.000687350.000740.00068520.000740.000673720.000690.00067450.00060.000639820.000670.000634230.000620.000623480.00060.000613170.00060.000630270.000640.000610740.000590.000619260.000580.000634420.000550.000619510.000680.000613376.5673
380.000950.000869910.000890.000890.000770.000809610.000860.000781460.000790.000790.000770.000736360.000770.000735270.000770.000724430.000720.000719650.000750.00068690.000720.000679530.000690.000666770.000690.000654690.000710.00067160.000650.000650.000660.000660.000640.000678560.000620.000659780.000660.000654494.1451
390.000960.000923230.000980.000942770.000930.000859870.000830.000830.000950.00084240.000910.000791020.000870.000791090.000880.000780770.000770.000770.000760.000739290.000730.000730.000730.00071510.000750.000700980.000770.000717710.000720.000693760.000690.000705320.000770.000727430.000720.000704550.00070.00074.8184
400.001010.000983250.001020.00100210.001110.000916410.001020.000884650.000910.000901040.001010.000851990.000930.000853310.000960.000843360.000870.000826160.000840.00079760.000850.000786230.000870.000769070.000780.000752590.000820.000769160.000790.000742550.000760.000755720.000820.000781530.000820.000754320.000770.000750386.9925
410.001170.00105080.001190.0010690.001150.000980050.001120.000946180.001070.000966680.000920.000920.001050.000922680.001020.000912880.001040.000888790.000890.000862490.000950.000848870.000870.000829320.000860.000810130.000890.000826570.000820.000796930.000890.000811790.000870.000841410.000870.000809640.000860.000806148.2581
420.001230.00112690.001250.00114420.001230.00105160.001220.00101550.001220.00104010.001090.000995850.0010.0010.001140.000990110.001080.000958640.001070.000934690.001030.000918650.001050.00089660.000970.000874290.000980.000890630.001010.000857540.000990.000874140.000940.000907690.000910.000871140.000950.0008678710.32
430.001310.00121260.00130.00122880.001370.00113220.001350.00109350.001260.00112240.001360.00108040.001190.00108620.001120.00107590.001240.00103650.001230.0010150.001180.000996390.001130.000971710.001110.000945810.001110.000962110.001080.000925110.001040.00094350.001010.000981060.001030.000939520.0010.0009361911.928
440.00160.00130910.001440.0013240.001470.00122290.001450.00118130.001430.00121440.001270.00117480.001460.00118230.001220.00117120.001140.00112340.001350.00110450.001270.0010830.001310.00105560.001180.00102560.001210.00104190.001140.00100040.001150.00102060.001120.00106230.001130.00101550.001160.001011812.606
450.001620.00141760.001610.00143110.001510.00132490.001540.00128010.001480.00131730.001460.001280.001370.00128940.001430.00127710.001330.00122030.001220.00120390.001440.00117950.001460.00114920.001350.00111450.00140.00113090.001310.00108440.001210.00110640.001260.00115220.001230.00110.001240.001095512.358
460.001750.00153990.001770.00155170.001780.00143960.001640.00139150.001570.00143260.001590.00139740.001560.00140880.001490.00139470.001490.00132840.001430.00131470.001320.00128690.001590.00125370.001470.00121360.001510.00123010.001430.0011780.001450.00120180.001340.00125170.001420.00119390.001320.001188212.703
470.002020.00167750.00190.00168730.001920.00156880.001850.00151680.001740.00156150.001760.00152830.001720.00154180.001620.00152530.001580.00144880.00170.00143780.001580.00140660.001430.00137040.001680.0013240.001690.00134090.001560.00128230.001540.00130790.001580.00136180.001490.00129830.001390.001290713.236
480.002160.00183250.002160.00183990.002130.00171410.001990.00165780.0020.00170580.001870.00167420.001870.00169010.00180.00167040.001820.00158320.001690.00157490.001880.001540.001790.00150070.001550.00144720.001880.00146450.001750.00139850.001730.00142590.001660.00148370.001590.00141440.001550.001404213.67
490.002480.00200690.002260.00201160.002270.00187750.002220.00181670.002230.00186730.002050.0018370.002030.00185540.0020.00183150.002050.0017330.002020.00172740.001870.00168850.001940.00164620.001770.00158450.001820.00160240.002030.00152810.001920.00155720.001870.00161860.001860.00154340.001770.001529914.426
500.002660.00220320.002570.00220480.002380.00206140.002440.00199540.002350.0020480.002210.00201850.002280.00203970.002190.00201050.002140.00190010.002060.00189710.00210.0018540.002050.00180860.00210.00173750.002030.00175630.001890.00167250.002160.00170310.002090.00176790.0020.00168670.001970.001668913.454
510.002870.00242420.002860.00242210.002690.00226820.002730.00219670.002580.00225020.002440.00222090.002390.0022450.002380.00220930.002250.00208640.002230.00208580.00230.00203820.002230.00198980.00210.00190810.002360.00192790.002080.00183340.0020.00186540.002390.00193310.002240.00184610.002140.001822812.343
520.002970.00267290.003060.00266660.002890.00250090.002890.00242320.002650.00247640.002690.00244650.002710.00247380.002430.002430.002610.00229410.002450.00229590.002390.00224350.002370.00219210.002350.00209830.002430.00211930.002560.00201280.00230.00204580.002120.00211590.002430.00202320.002360.00199310.381
530.00330.00295280.003190.00294160.003190.00276270.003060.00267810.002970.00272950.002820.00269810.002780.00272880.002790.00267510.00260.00252560.002850.00252950.002550.0024720.002570.00241790.002650.00231020.002620.00233290.002460.00221270.002570.00224650.002470.00231830.002220.002220.002650.00218158.2047
540.003390.00326780.003420.00325090.003240.0030570.003370.0029650.003260.00301260.003260.00297860.003070.00301290.003040.00294740.002760.00278380.002970.00278940.002930.00272660.002670.002670.002720.00254640.002820.00257110.002750.00243540.002540.00246960.002770.00254220.002650.00243870.002390.002395.6231
550.003790.00362230.003820.00359880.003730.00338810.003430.00328790.003520.00332940.003380.00329140.003380.00332950.003240.00324960.003160.00307160.003180.00307850.003010.003010.00310.00295130.00260.00280970.003090.00283690.002890.00268360.002850.00271760.002790.002790.003010.00268180.002840.00262074.7793
560.004150.00402120.003990.003990.003770.00376050.003860.00365120.003660.00368370.003640.003640.003520.00368220.003610.00358530.00340.00339240.00340.00340.00350.00332560.003250.00326530.003320.00310310.003110.00313320.002990.00296020.003070.00299340.003140.00306420.003020.0029520.003010.00287612.1195
570.004470.004470.004480.004430.004140.00417920.004020.004060.004080.004080.003890.00402860.003850.00407520.003790.00395790.003750.003750.003560.00375760.003530.00367710.003640.00361560.003430.003430.003590.00346380.003160.00326830.00330.00330.003280.00336750.003260.00325210.002970.00315862.289
580.004920.00497490.004740.00492460.004650.004650.004520.004520.004180.00452320.004410.00446170.004150.00451290.004270.00437160.00390.00414860.004090.00415530.003980.00406830.003860.00400650.003720.00379430.00360.00383240.003610.00361160.003310.00364080.003420.00370310.003570.00358560.003430.00347113.574
590.00540.00554280.005070.00548080.00510.00517930.005030.00503740.004540.00501890.004380.00494440.004590.00500050.004390.00483080.004470.00459280.00440.00459760.004410.00450390.004310.00444270.004120.00420010.004240.00424340.003920.0039940.003950.00401960.003610.00407430.00390.00395620.003680.00381694.79
600.005930.00618150.005740.0061060.005530.00577430.005320.00561950.005130.00557310.005130.00548240.005020.00554350.004830.00534050.00480.00508770.004680.00508940.004820.00498880.00480.00492930.004360.00465230.004440.00470170.004420.004420.004170.00444070.004320.0044850.004050.00436780.003810.00419946.2674
610.006560.00689980.006470.00680860.006030.0064430.005940.0062740.005580.00619270.005420.00608170.005550.00614830.005280.00590620.005320.00563930.005150.00563610.005280.00552840.004980.00547210.004940.0051560.00520.00521260.004790.00489450.004620.00490870.00440.00493930.004560.0048250.003950.00462257.7306
620.007230.00770740.00720.00759830.006650.00719460.006580.00701010.006260.00688540.006070.00674950.005870.00682170.005630.00653390.005630.00625370.00560.00624390.005510.00612910.005670.00607750.00550.0057170.005520.00578210.005140.00542290.005040.00542870.004930.00544170.004870.00533290.004720.00509058.9977
630.007810.00861520.008080.00848550.007290.0080390.00750.00783760.006970.00765960.006650.00749330.006620.00757140.00640.00723040.006080.00693820.006020.00691950.00620.00679740.005990.00675270.005960.00634190.005870.0064170.005780.00601140.005390.00600650.005330.00599730.005450.0058970.005090.00560810.185
640.0090.00963550.00830.00948210.008430.00898760.008070.00876790.00760.00852480.007370.00832170.007170.00840590.006910.00800310.006890.00770060.006580.00767030.006670.0075410.006750.00750560.006240.00703770.006550.00712440.006140.00666660.00640.00664840.005830.00661160.00590.00652330.005640.006180411.308
650.009760.0107820.009540.0106010.009110.0100530.0090.00981330.008560.00949140.007980.00924410.007950.00933460.007640.00886020.007520.00854950.007320.00850460.007380.00836820.007050.0083450.007040.00781230.007080.00791280.006760.0073960.006560.00736150.006770.00729090.006340.00721880.006220.006813212.536
660.010930.012070.010760.0118580.010140.0112490.009880.0109880.009530.0105710.008740.0102710.008930.0103680.008570.00981070.008350.00949480.008080.00943150.008070.0092882