multivariate linear time series

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1、Tsay-Driver-12013/10/2811:18page1#1CHAPTER1MultivariateLinearTimeSeries1.1INTRODUCTIONMultivariatetimeseriesanalysisconsiderssimultaneouslymultipletimeseries.Itisabranchofmultivariatestatisticalanalysisbutdealsspecificallywithdependentdata.Itis,ingeneral,muchmorecomplicatedthantheunivariatetime

2、seriesanalysis,especiallywhenthenumberofseriesconsideredislarge.Westudythismorecom-plicatedstatisticalanalysisinthisbookbecauseinreallifedecisionsofteninvolvemultipleinter-relatedfactorsorvariables.Understandingtherelationshipsbetweenthosefactorsandprovidingaccuratepredictionsofthosevariablesareva

3、luableindecisionmaking.Theobjectivesofmultivariatetimeseriesanalysisthusinclude1.Tostudythedynamicrelationshipsbetweenvariables2.ToimprovetheaccuracyofpredictionLetz=(z,···,z)beak-dimensionaltimeseriesobservedatequallyt1tktspacedtimepoints.Forexample,letz1tbethequarterlyU.S.realgrossdomesticprodu

4、ct(GDP)andz2tthequarterlyU.S.civilianunemploymentrate.Bystudyingz1tandz2tjointly,wecanassessthetemporalandcontemporaneousdependencebetweenGDPandunemploymentrate.Inthisparticularcase,k=2andthetwovariablesareknowntobeinstantaneouslynegativelycorrelated.Figure1.1showsthetimeplotsofquarterlyU.S.realGD

5、P(inlogarithmofbillionsofchained2005dollars)andunemploymentrate,obtainedviamonthlydatawithaveraging,from1948to2011.Bothseriesareseasonallyadjusted.Figure1.2showsthetimeplotsoftherealGDPgrowthrateandthechangesinunemploymentratefromthesecondquarterof1948tothefourthquarterof2011.Figure1.3showsthescat

6、terplotofthetwotimeseriesgiveninFigure1.2.Fromthesefigures,wecanseethattheGDPMultivariateTimeSeriesAnalysis:WithRandFinancialApplications,FirstEdition.RueyS.Tsay.c2014JohnWiley&Sons,Inc.Published2014byJohnWiley&Sons,Inc.1Tsay-Driver-12013/10/2811:18page2#22multivariatelineartimeseriesln(GD

7、P)7.58.59.51950196019701980199020002010YearUnrate4681950196019701980199020002010YearFIGURE1.1TimeplotsofU.S.quarterlyrealGDP(inlogarithm)andunemploymentratefrom1948to2011.Thedataareseasonallyadjusted.GDPgrowth0.0