Model selection and order determination for time series by information between the past and

Model selection and order determination for time series by information between the past and

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頁數(shù)：26頁

時間：2019-05-27

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1、ModelSelectionandOrderDeterminationforTimeSeriesbyInformationBetweenthePastandtheFutureLeiLi(DepartmentofStatistics,UniversityofCalifornia,BerkeleyCA94720)ZhongjieXie(DepartmentofProbabilityandStatistics,PekingUniversity)TypesetbyAS-TXME12AbstractInthispaper,theinformationbetweenthepasta

2、ndthefutureofaGauss-ianstationarysequenceiscalculatedeitherbyitsspectraldensityorbyitsautocovariances,andisrelatedtotheproblemofmodel tting.Itisdemon-stratedthatthecriterionofminimummutualinformationisthegeneralizationofthatofmaximumentropy.Byemployingtheaboveinformationquantity,wepropos

3、edaprocedure,whichiscalledLICforsimplicity,toobtainconsistentestimateoftheorderoftheBloom eldmodelortheautoregressivemodel.InMonteCarlostudies,weillustratetheLICprocedurebyseveralexamples,andalsoestimatespectraldensityoftimeseriesbytheBloom eldmodelandLICmethod.KeyWordsandPhrases:timeser

4、ies,information,parametricmodels,orderselection.3x1IntroductionThemainpurposeofthispaperistoexhibitsomeapplicationsofthemutualinformation(thatbetweenthepastandthefutureoftimeseries)inthe eldsofparametricmodelling.SupposethatxisaGaussianstationaryseries,itiswellknownthatitstentropyH(x)pla

5、ysaveryimportantroleinthemodel ttingproblem.Anothertinformationquantity,theinformationbetweenthepastLfx;stgandthesfutureLfx;s>tg,whichwedenotedbyp-finformationforsimplicity,hassalsobeende nedanddiscussedinIbragimovandRozanov(1978).FollowingtheworksofJewellandBloom eld(1983a,1983b),insec

6、tion2ofthepresentpaper,someformulasforcalculatingthep-finformationbyeitherthespectraldensityfunctionortheautocovariancefunctionsareobtainedbytheauthors.InSection3,weconsiderthemodel ttingproblemunderthecriterionofminimump-finformationandpresentsomeinterestingresults:1.If;;;,thevalueso

7、fthe rstp+1autocoviancefunctions,havebeen01pgiven,thenunderthereferredcriterion,theoptimum ttingofxmustbeantAR(p)model,whichcoincideswiththeresultunderthecriterionofmaximumentropy.2..Supposethatxisaregularstationaryseries,thenasshownbySzego,tKolmogorovandKrein,ithasaspect

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