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1、Tsay-Driver-12013/10/2813:37page333#1CHAPTER6FactorModelsandSelectedTopicsInthischapter,weconsidersomeselectedtopicsinmultivariatetimeseriesanalysisthatareofpracticalimportanceandtheoreticalinterest.Thetopicsdiscussedincludeseasonalmodels,principalcomponentanalysis(P
2、CA),useofexogenousvariables,factormodels,missingvalues,andclassificationandclusteringanalysis.Forsometopics,thetreatmentisbriefastheyareeitherwellknownorstillunderintensiveinvestigationintheliterature.Forinstance,thetreatmentofseasonalmodelsisbriefbecauseitinvolvesdirecte
3、xtensionsoftheunivariatemodels.Specialattentionispaidtofactormodels.Weprovideacomprehensivedescriptionofthefactormod-elsavailableintheliteratureanddiscusssomeoftheirpropertiesandlimitations.Wealsoconsiderasymptoticprincipalcomponentanalysis.Forclusteringanalysis,wefocuso
4、nthemodel-basedapproachinwhichaunivariateARmodelisusedforallseriesinagivencluster.Moreelaboratemodelsforclassificationcanbeenter-tainedattheexpenseofincreasedcomputationandharderpriorelicitation.Again,realexamplesareusedtodemonstratetheanalyses.6.1SEASONALMODELSSeasonalit
5、yoccursinmanyeconomic,financial,andenvironmentaltimeseries.Thequarterlyearningspershareofacompanytendtoexhibitanannualcyclicpattern.Theunemploymentratesofacountryoftenshowasummereffectasmanystudentsseeksummerinternjobs.Ofcourse,dailytemperatureofagivenlocationintheUnitedS
6、tates,criticaltodemandsofelectricityandnaturalgas,isseasonal.ManyeconomicdatapublishedintheUnitedStatesareseasonallyadjusted.However,itiswellknownthatthesamplespectraldensityfunctionofaseasonallyadjustedseriesviamostseasonaladjustmentmethods,forexample,themodel-basedX-12
7、procedure,hasatroughattheseasonalfrequency,implyingthatsomeMultivariateTimeSeriesAnalysis:WithRandFinancialApplications,FirstEdition.RueyS.Tsay.c2014JohnWiley&Sons,Inc.Published2014byJohnWiley&Sons,Inc.333Tsay-Driver-12013/10/2813:37page334#2334factormodelsandse
8、lectedtopicsseasonalityremainsinthedata.See,forinstance,theU.S.monthlyunemploymentrateanalyzedinTsay(20
