指数平滑法初始值计算与平滑系数选取的新方法-何舒华

10220114JournalofGuangzhouUniversityNaturalScienceEditi[e-mail]1671-4229201102-0006-05510000t*t＜=t*t＞t*k50%α．O213A19591－3．．S0α．S0α4－8．11．y1y2…yt－1ytSty1y2…yt－1ytSt=αyt+1－αSt－11SttyttSt－1t－1α0＜a＜1．1St=αyt+1－ααyt－1+1－αSt－2=αyt+α1－αyt－1+1－α2St－2=αyt+α1－αyt－1+α1－α2yt－2+…+α1－αt－1y1+1－αtS0=α∑t－1j=01－αjyt－j+1－αtS02β=1－α0＜β＜1St=αyt+αβyt－1+αβ2yt－2+…+αβt－1y1+βtS0=α∑t－1j=0βjyt－j+βtS031、23．ω0=βtω0S0．ωj=αβt－jj=t…21ωjyj1＞ωt＞ωt－1＞ωt－2＞…＞ω2＞ω1＞0．S0St1y1S0S0Stα=0.1t=10ω0=βt=1－0.110=0.3486784ω10=a=0.1α=0.05t=10ω0=βt=1－0.0510=0.598737ω10=a=0.05S0ω02ytωty1S0y1ω1ωt．2St．αSt．y1S0St=αyt+α1－αyt－1+α1－α2yt－2+…α1－αt－1y1+1－αtS0|S0=y14StS0St1=αyt+α1－αyt－1+α1－α2yt－2+…α1－αt－1y1+1－αtS0|S0=St5St1S0St2=αyt+α1－αyt－1+α1－α2yt－2+…α1－αt－1y1+1－αtS0|S0=St16mStm－1S0Stm=αyt+α1－αyt－1+α1－α2yt－2+…α1－αt－1y1+1－αtS0|S0=Stm－17mStmStm－1．Stmytyt－1…y1．S0ω00ωtωt－1…ω1．4～7ωtωt－1…ω1ω0St=αyt+αβyt－1+αβ2yt－2+…+αβt－1y1+βtS0S1t=αyt+αβyt－1+αβ2yt－2+…+αβt－1y1+βtαyt+αβyt－1+αβ2yt－2+…+βtS0=1+βtαyt+αβyt－1+αβ2yt－2+…αβt－1y1+β2tS08S2t=αyt+αβyt－1+αβ2yt－2+…+αβt－1y1+βt1+βtαyt+αβyt－1+…+β2tS0=1+βt+β2tαyt+αβyt－1+αβ2yt－2+…+αβt－1y1+β3tS09mStmStm=1+βt+β2t+…+βmtαyt+αβyt－1+…+αβt－1y1+βm+1tS010C=1+βt+β2t+…+βmtStm=Cαyt+αβyt－1+αβ2yt－2+…+αβt－1y1+βm+1tS011βm+1t0Smt≈Cαyt+αβyt－1+αβ2yt－2+…+αβt－1y112ytyt－1…y1CαCαβCαβ2…Cαβt－1C=1+βt+β2t+…+βmt=1－βm+1t/1－βt≈1/1－βtSt≈α1－βtyt+αβ1－βtyt－1+αβ21－βtyt－2+…+αβt－11－βty1133St=αyt+α1－αyt－1+α1－α2yt－2+…+α1－αt－1y1α+α1－α+α1－α2+…+α1－αt－1=α∑t－1j=01－αjyt－jα∑t－1j=01－αj14α∑t－1j=01－αj=α∑t－1j=0βj=1－βtSt=α1－βtyt+αβ1－βtyt－1+αβ21－βtyt－2+…+αβt－11－βty1154．St=yt+βyt－1+β2yt－2+…+βt－1y11+β+β2+…+βt－1=∑t－1j=0βtyt－j∑t－1j=0βt∑t－1j=0βt=1+β+β2+…+βt－1=1－βt/1－β=1－βt/α710St=∑t－1j=0βtyt－j∑t－1j=0βt=α1－βt∑t－1j=0βtyt－j=αα－βtyt+αβ1－βtyt－1+αβ21－βtyt－2+…+αβt－11－βty116t=10α=0．1i=123…10、1．1Table1Thecomparisonofweightasiterationsincreasetiα=0．1β=0．9i=1i=2i=3…i=9i=100w00．34870．12160．0424…0．00010．0000tt1ω10．03870．05230．0570…0．05950．059510．03870．059510．38740．05952ω20．04300．05810．0633…0．06610．066120．04300．066120．43050．06613ω30．04780．06450．0703…0．07340．073430．04780．073430．47830．07344ω40．05310．07170．0781…0．08160．081640．05310．081640．53140．08165ω50．05900．07960．0868…0．09070．090750．05900．090750．59050．09076ω60．06560．08850．0965…0．10070．100760．06560．100760．65610．10077ω70．07290．09830．1072…0．11190．111970．07290．111970．72900．11198ω80．08100．10920．1191…0．12440．124480．08100．124480．81000．12449ω90．09000．12140．1323…0．13820．138290．09000．138290．90000．138210ω100．10000．13490．1470…0．15350．1535100．10000．1535101．00000．15351．00001．00001．0000…1．00001．00000．65131．00006．51321．0000StS0ω00ytyt－1…y1．αSt．tω0=βtωtω0S0．ω*0=0．1ωtt*=log0.1α/log1－αt*．t*St．2α1αα．αααt≤10α．2α2α．①kytyt－1…yt－k+1≥80%αβ．kytyt－1…82yt－k+1Sk=α1－βk1－βtytyt－1…y1St=α1－βt1－βkPk=SkSt=1－βk1－βt．1－βk=0．81－βt≤1k=1－βk1－βt≥0．8．2、3tkk0.8．2kβtkPkTable2AccumulativecontributionratePkofthemostrecent510dataunderdifferentcorrespondingandvaluekβt=20t=40t=6050．7248Pk=0．8013Pk=0．8000Pk=0．8000100．8513Pk=0．8334Pk=0．8014Pk=0．8000β0.7248α=0.27525≥80%β0.8513α=0.148710≥80%．②nn+150%βn．1yt12yt－1nn+1yt－nααβαβ2…αβn．βn=0.5nn+1yt－n1yt50%ββ=0.51/nαα=1－β．3n=3510βαTable3CorrespondingvalueofβandαwhenHLhalf－lifenequalsto3510respectivelynβα30．79370．206350．87060．1294100．93300．0670α=0．2063β=0．79373+1yt－3150%n=3α=0．1294β=0．87065+1yt－5150%n=5．k≥80%n+150%n=αβα．③^yt+1=St=αyt+1－α^yt=^yt+αyt－^yty⌒t+1yt－y⌒ty⌒t．α．31αS0StS0．2tαSt．t＞t*t*St．3k≥80%n50%αn=αα．910References1DENGJi-xianYANGWei-quanXULiu-jun．MathematicalmethodsofeconomicforecastanddecisionmakingM．GuangzhouSunYat-senUniversityPress1986．inChinese2FENGWen-quan．TechnologyofeconomicforecastanddecisionmakingM．WuhanWuhanUniversityPress1994．inChinese3LIXin-yu．StatisticsforbusinessandeconomicsM．BeijingBeijingUniversityPress1999．inChinese4HANDe-zhong．AnoptimizationofthesmoothcoefficientJ．StatisticalResearch1993650-52．inChinese5TANGYan-sen．ExponentialsmoothingforecastingformulaandsmoothingcoefficientJ．Statistics＆InformationTribunes1998138-43．inChinese6WANGChang-jiang．SelectionofsmoothingcoefficientviaexponentialsmoothingalgorithmJ．JournalofNorthUniversityofChinaNaturalScienceEdition2006276558-561．inChinese7SHANYi-binJINMing．AboutdeterminationofsmoothingcoefficientandinitialvalueJ．JournalofDalianUniversity199772175-177．inChinese8LIBing-zhou．AdiscussionaboutthemathematicalprincipleofexponentialsmoothingJ．JournalofChang＇anUniversityNaturalScienceEdition198644151-160．inChinese1．M．1986．2．M．1994．3．M．1999．4．J．1993650-52．5．J．1998138-43．6．J．2006276558-561．7．J．199772175-177．8．J．198644151-160．ThenewmethodsofcalculatinginitialvalueandselectingsmoothingcoefficientinexponentialsmoothingHEShu-huaHEAi-linInvestmentDirectorOAKINVESCOGuangzhouLimitedGuangzhou510000ChinaAbstractThispaperprovesthataftertimesofiterationstheresultsfromexponentialsmoothingmethodcouldrapidlyapproachthoseresultsformexponentweightedaveragemethod．Itfurtherproposestheuseofdifferentmethodstocalculateexponentialsmoothingvalueaccordingtodataamountwhent＜=t*t*referstothemin-imumdataamountforrecurrencealgorithmiterationsorfullexponentweightedaveragemethodisu