ARIMA模型在煤炭消费预测中的应用分析

23[e-mail]:100888572007020011707ARIMA池启水1,刘晓雪21.,100081;2.,100081:煤炭属于重要的民用能源，对其消费量进行预测，可为合理安排煤炭生产提供依据，优化社会资源的配置。采用Box和Jenkins的ARIMA模型，对1953年以来我国煤炭消费量的年度数据进行分析。与结构性因果模型、自回归AR、移动平均MA、自回归移动平均ARMA模型等相比较，ARIMA模型不但适合于我国煤炭消费量的非平稳时间序列的特点，并且预测效果比较理想。结果表明，ARIMA3,1,3模型的预测效果良好，2002年~2005年平均预测误差仅为3.981%，可用于未来我国煤炭消费量的预测。:煤炭消费;ARIMA;预测与分析;时间序列:F407.215;TE01:AARMAARMA[1]ARIMA1953~2005EViews5.01ARIMAARIMAautoregressiveintegratedmovingaveragemodelBoxJenkinsBJBoxJenkinsmodelARIMA[2]1.1ARIMAintegrationdxtd()1dttwLx=−wt200723118wtARMAp,q1111ttptpttqtqwcwwφφεθεθε−−−−=++⋅⋅⋅++++⋅⋅⋅+()()ttLwcLΦΘε=+()2121ppLLLLΦφφφ=−−−⋅⋅⋅−()2121qqLLLLΘθθθ=+++⋅⋅⋅+ARMAp,qdARIMAp,d,qLagrangeARMAp,q()()()1dttLLxcLΦΘε−=+1.2ARIMAARIMA(p,d,q)ARMAACPACARMApq[3]ARIMAp,d,qtARIMAp,d,q1whitenoise2ARIMA2.1pq()tEuµ=;()2vartuσ=;()cov,ttssuuγ−=tsARMAp,q[4]{xt}{xt}1E{Xt}var{Xt}cov{Xt}tADFPP{Xt}2池启水,等:ARIMA1190500001000001500002000001591317212529333741454953{Xt}yt=logXt{Yt}ADF{Yt}PP{Yt}{Zt}={Yt}{Yt1}{Zt}ADFPP{Xt}{Yt}{Zt}11{xt}Fig.1Linegraphof{xt}series1Table1Resultofseriesunitroottest{Xt}{Yt}{Zt}C,T,KC,T,0C,T,00,0,01%4.1484655.0916752.6110945%3.5004954.1525111.94738110%3.1796173.5123731.612725ADFADF1.2292283.1806994.011546C,T,KC,T,0C,T,00,0,01%4.1445844.1445842.6110945%3.4986923.4986921.94738110%3.1785783.1785781.612725PPPP0.2765623.0843143.741058C,T,KCTK01{Xt}ADF1.2292281%5%10%{Xt}PPPP1%5%10%{Yt}ADFPPPP3.0843141%5%10%{Zt}ADFPP4.013.7499%ADFPPARMAACFPACF{Zt}ACPAC2225%0213200723120pp=313qq=32{Zt}12Fig.2Correlationof{Zt}seriesfrom1to12laggedrank2.2ARIMAId1d1{Zt}2Zt2Table2EstimationoutputtPC0.0509610.00332215.338600.0000AR10.4904290.1579953.1040850.0033AR30.1635310.1221581.3386790.1876MA10.3398170.1171692.9002340.0058MA30.6540860.1029166.3555280.0000R20.5475830.059935R20.5064540.1383250.0971771.7281130.4155091.53507047.33876F13.31385DW1.964375F0.000000CAR1AR3MA3AkaikeAIC[5]AIC1.728113AIC10.4080.4089.16400.00220.0740.1119.46750.00930.3690.43417.2900.00140.1620.23718.8230.00150.0580.01519.0240.00260.0660.16319.2900.00470.0690.06719.5840.00780.2030.18222.2020.00590.2160.05525.2440.003100.0300.08925.3020.005110.1070.07626.0920.006120.1460.01827.5920.006ACPACQP2池启水,等:ARIMA121R2=0.552R)=0.51S.E0.097ARIMA3,1,3{Zt}{Zt}33ADF[6]ARIMA0,0,0ARIMA3,1,3{Zt}ADF3.291%5%10%3{Zt}Fig.3Goodnessoffit3Table3ResultofunitroottestofresidualseriestPADF3.2909460.00151%2.6140295%1.94781610%1.6124922.32{Zt}ARIMA3,1,313130.0509610.4904290.1635310.3398170.654086tttttZZZεε−−−−=+−−−{}tYARIMA3,1,3113130.0509610.4904290.1635310.3398170.654086ttttttZYZZεε−−−−−=++−−−{Xt}113130.0509610.4904290.1635310.3398170.654086exp()ttttttYZZXεε−−−−−++−−−={Xt}2002~20052006443.110%~4.375%2001~20053.981%ARIMA3,1,3-0.6-0.4-0.200.20.40.60.815913172125293337414549t20072312242002~2005Table4Comparisonbetweenforecastingandactualcoalconsumptionsfrom2002to2005(pertenthousandstonsofstandardfuel,%)20022003200420052006t105044.9114516.0143879.9158652.0160181.8t100641.4119693.2138194.4153866.8t4403.55177.25685.54785.24.3754.3254.1143.1103ARIMAARMAARIMAttARIMAARIMAtARIMA1953tARIMA3,1,313132001~2005ARIMA3,1,33.110%~4.375%2002~20053.981%ARIMAARIMA3,1,3:[1]FANJ,YAOQ.Nonlineartimeseries:NonparametricandparametricmethodsM.Beijing:SciencePress,2006,1013.[2]BOXG,JENKINSG.Timeseriesanalysis,forecasting,andcontrolM.SanFrancisco:HoldenDay,1970,111.[3]BOXG,JENKINSG.,MACGREGORJ.Somerecentadvancesinforecastingandcontrol,PartTwoJ.Statist,1974,4:158179.[4]ADAKS.Time-dependentspectralanalysisofnon-stationarytimeseriesJ.JournalofAmericanStatisticalAssociation,1998,93:14881501.2池启水,等:ARIMA123[5]AKAIKEH,Cononicialcorrelationanalysisoftimeseriesandtheuseofaninformationcriterion,insystemsidentification:AdvancesandcasestudiesM.NewYork:AcademicPress,1976,2796.[6]DICKEYD,FULLERW.DistributionoftheestimatorsforautoregressivetimeserieswithaunitrootJ.JournaloftheAmericanStatisticalAssociation,1979,74:427431.[7].中国统计年鉴R.1978~2006.StudyontheapplicationofARIMAModelinforecastingChina’scoalconsumptionCHIQi-shui1,LIUXiao-xue21.InstituteofDefenseEconomicsandManagement,CentralUniversityofFinanceandEconomics,Beijing,100081,China;2.Collegeofstatistics,CentralUniversityofFinanceandEconomics,Beijing,100081,ChinaAbstract:Coalbelongstooneoftheimportantcivilenergysources.Forecastandanalysesoncoalconsumptioncanhelpmakereasonablearrangementsincoalproductionandoptimizethecollocationofsocialresources.ThispaperusestheARIMAmodelwhichwasadvancedbyBoxandJenkinstoanalyzeannualdataofcoalconsumptioninChina.TheoriginaldataareprovidedbyChinaStatisticsYearbook.Unlikemodelssuchasthestructureanalysisofcauseandeffect,theautoregressivemethodAR,andthemovingaveragemethodMA,theARIMAmodelisnotonlysuitablefortheanalysisofcoalconsumptioninChina,whichisnotabalancedtimeseries,butalsoitsforecastingeffectisexact.ThispaperconcludesthattheforecastapplyingARIMA3,1,3,whichforecastingerroronly3.981percentfrom2002to2005,isexactandtheAMIMAmodelcanbeusedtoforecastshort-termofcoalconsumptioninChina.KeyWords:coalconsumption;ARIMA;forecastandanalysis;ti