有关失业率的时间序列分析和回归分析.docx

有关失业率的时间序列分析和回归分析.docx

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有关失业率的时间序列分析和回归分析

TheUnemploymentRate

Summary

Unemploymentratereflectstheemploymentsituationofacountryoradistrict.Itispossiblethatsomecountrieshavesimilartimeseriesinunemploymentrate.Wewanttodividethesecountriesintoservalclasses,andthenwecanpredicttheemploymentrateofspecialclassandstudythefactorsinfluencingunemploymentrate.

Wecomputemeanandvarianeeofunemploymentrateindifferentregions,andsortthemindependently.Fromtheaboveresults,weknowthatSpain,PolandandBulgariahavebiggervaluesinabovetwostatisticsthantheothers,whichrevealsthesegovernmentsperformedbadlyinemployment.

WeusetheSystemClustermethodtodivide35countriesintofourlevelsaccordingtopseudoFstatistic.Thesameclassdataillustratethatthesecountriesarecommoninunemploymentrate,especially,Spainisaclassalone.

TakingunemploymentdataofChinaasexample,wesolvethisproblemwithtimeseriesaftermakingoriginaldatastationary.WeselecttheappropriatemodelthroughAICandSBCstatistics,andthenwegetthetrendequation.Whentestingthequalityoffitting,weobtaintheMPEAstatisticwhichis3.51%,thuswethinktheequationperformswell.SowepredictURin2011and2012,comparingwiththemeasuringvalues,itissurprisedthatpredictingvaluesissameasmeasuringvalues.Atend,werepeattheaboveprocesswiththedataofJapanandAustralia.

Forstrugglingwithmulticollinearityandnonlinearityalwaysexistingineconomicdata,weuseRFR（randomforestsregression）method.BycomparingR-Square,MSEandMPEA,weobtainthattheRFRismoreaccuracythanOLSR.Inordertoillustratetheimportaneeofindependentvariables,wedefineastatisticasacriterion.

WeuseClusterAnalysis,TimeSeriesAnalysisandtheRandomForestsRegressiontoanalyzetheunemploymentrateamongdifferentregions.

Keywords:

SystemCluster;TimeSeries;RFR;OLSR;

1.Introduction

Twoyearsafterwewillfindajob,atthattime,theunemploymentratewillbeassociatedwithus.Nowletusexploretheunemploymentrate.

Unemploymentrateisanimportantindexofthecapitalmarket,isalaggingindicatorcategory.Theincreaseinunemploymentisaweakeconomysignal,canstimulateeconomicgrowth.Onthecontrary,theunemploymentratedroppedwillbetheformationofinflation.

Weanalyzethesituationofallcountries,thefurtherresearchwillgetthelevelofunemploymentrateinallcountries,andthenwepredictthetendencyofunemploymentrate

2.Notations

Table1indicators

Indicator

meanings

GDP

GrossDomesticProduct

FS

PublicFinanceExpenditure

M2

CurrencySupply

EP

TheEconomicActivity

PC

PeopleFinalConsumption

CPI

ConsumerPriceIndex

EG

EnergyConsumption

UR

RateofUnemployment

3.MeanandVarianceofUnemploymentRate

Themeanofunemploymentratereflectsthelevelofeconomicdevelopment,whengettingthemeanofURamong35countries,wecandiscoverthefactthatthemeanofURchangefromlessthan2%tomorethan14%,whichillustratesclearlythatlevelsofunemploymentratearedifferentamongthesecountries.Thefigure1canhelpusseethatwell.WearesurprisedatSpainwhoseunemploymentrateachieves15.39%.

TheMeanofUR

in

country

Figurelthemeaningsofindicators

Inreality,differentcountriesowndifferentlevelofdevelopmentsothatthevalueofURisnotaconstant.Therefore,wewantfurthertoknowtheURvarianeewhichrevealtheeconomicstability.Thefigure2reflexesthatthevolatilityofvarianeeofdifferentcountries.

TheVarianceofUR

ChinaBulgariaGermanyIsraelNorwayRussiaBritain

country

Figure2VarianeeofUR

Atthelast,wegainthetopthreeofURmeanandvarianee,asfollow:

Table2Topthreeoftwoindicators.

country

Spain

Poland

Bulgaria

mean

15.39

14.22

13.76

country

Spain

Bulgaria

Poland

varianee

29.66

18.76

13.04

Fromtable2,weseethatSpain,PolandandBulgariaarethetopthreebothofthetwoindicators,that'stlwseyjovernmentsdidbadlyinthefieldofemployment,andtheireconomicenvironmentisunstable.

4.SystemClusterAnalysis

Nowweanalyzetheunemploymentrate,whethertheyareatasimilarlevel,weutilizeClusterAnalysistoclassify[1].

4.1Expressthedistancebetweencountries

ThefollowformuladescribesthedistaneebetweentwopointsusingEuclideandistanee,

i

（p2

dj=Z（诲-Xjk）

（1）

Ik」丿

AdvantageofEuclideandistaneeiswhentheaxisorthogonalrotation,theEuclideandistanceismaintained.

4.2Thedistanceamongclasses

Hereweselecttheaveragelinkagemethodtoexpressthedistanceforbothofclasses.Usingaveragelinkagemethodisagoodwayofallthesamplesbetweeninformation

Where%andnLarerespectivelystandforthenumberofsamplesinclassesGkandGL.Theindexd0isthedistancebetweenthesamplesiinGkandthesamplejinGk.

4.3TheClassingStatistic

Wesetupnasthetotalnumberofsamples,dividingoriginalsampleintokclasses,eachclasshavenisamplesandwederivethepseudoFstatistic:

厂W-R/k-1

Pk/n-k

Where

n'

W二'Xj_X]〔Xj「X

k#

Pk八Wi

i=1

ni

ThebiggerPseudoFstatisticvalueandthesmallerkvalueisthebettereffectofclassification.

Weobtaintheexaminationappealthroughclusteringanalysismethod,asshowninthedifferentnumberofclustersofStatistics.

Table3theinformationofcluster

Numbersofclusters

1

2

3

4

PseudoFstatistic

0

19.3

12.6

23.8

Numbersofclusters

5

6

7

8

PseudoFstatistic

19.3

17.3

15.1

19.5

Fromtable3,wefindthatwhenwedivideoriginalsampleintofourclasses,thepseudoFstatisticachievesthebestvalueaswellasth@valueisnotbig,thuswechoosethenumberofclassesasfour.Intheend,wegivethesystemdiagram.

Sp^ln

Poland

Bulgaria

Ireland

Russia

Turkey

Philippines

Israel

Germany

Greece

llaly

France

Finland

Romania

U.S.A

Sweden

Portugal

Hungaiy

Canads

New-Zealand

Denmark

Britain

Australia

Czech

Thailand

Norway

Holland

Iceland

ChiIna-Macao

China-Hongkong

Korea

Auslrla

Japan

China

0.00.51.D1.5

A^rag-eDigtancpBetw&e-niClusters

Figure3theclassresult

Ifclassifyingoriginalsampleintofour,thenwecometotheconclusionasfollows:

thefirstclassification:

China,Japan,Austria,SouthKorea,China

HongKong,Macao,Iceland,Holland,Norway,Thailand,Czech.Thesecondclassification:

Australia,Britain,Canada,NewZealand,Denmark,Hungary,Portugal,Sweden,Romania,Finland,American,France,Italy,Greece,Germany,Israel,Philippines,Turkey,Russia,Ireland

Thethirdclassification:

Bulgaria,Poland,Venezuela

Theforthclassification:

Spain

Weknowthattheunemploymentrateindexreflectstheoverallstateoftheeconomy,anditistheeconomicdataforeachmonthwithfirstpublished,sotheunemploymentrateindexcalledalleconomicindicatorsofthe"crownjewel".Itisforthemonthlyeconomicindicatorssensitiveonthemarket.

5.TimeSeriesModel

Atimeseries[2]isasetofobservationsxt,eachonebeingrecordataspecifictimet,andobserveddata{xt}isaspecificationofjointdistributions（orpossiblyonlymeansandcovarianee）ofasequenceofrandomvariables[Xt}ofwhich{xt}ispostulatedtoberealization.

5.1StationaryTest

Ifwewanttomakeagoodtimeseriesmodel,weshouldrecognizeitfirstly.Akeyroleintimeseriesanalysisisplayedbyprocesswhoseproperties,orsomeofthem,donotvarywithtime.

WechoosethedataofChinaasexampleandcurvethigure4

china

Figure4thescatterofUR

Formfigure4,wecanfindthattherateofunemploymentofChinahasincreasedtrendwiththetimegoing,thusweneedtomakeitstationarybeforeweconstructmodel.

5.2Stationaryprocess

Weproceedtomakethetimesequencestationarywiththefirstdifference,andwegivethescatterdiagram

dchlna

2

Figure5thescatterafterdifference

Fromthefigure5,weperceivethedatatendtostationary,whichsuggestthatwecanconstructtimeseriesmodel.

5.3TheARMAModel

WemakeanARMAtofitthedataofChinaUR,themodelisasfollows:

nm

Xt八讥」*t八jt_j

idjd（4）

TheparameteriofformulaisanautomaticregressionparameterofARMA,parameter咼isamovingaverage.ParametertisaStochasticProcesswithazeromeanandanormalwhitenoise,thats'o

2

say,tNo,；「a

Especially,whenm=0,themodelARMAn,missameasARn,theformulaisasfollows:

nXt=嘉：

卩iXt4*t

=（5）

InordertomakesuretheparametersofARMA,wegivetheautocorrelationfigure6.

Figure6thePACFandACF

Fromthefigure6,wecanfindtheautocorrelationcoefficientisfirsttruncationandthefirstpartialcorrelationcoefficientistwotimesthanstandarderror.SowepreliminarymakeitasAR

（1）orMA

（1）.

Tomakesurewhichmodelisbetter,wecomputesomestatisticsoftwomodels.

TheinformationofmodelAR

（1）

Table4theARinformationofAICandBIC

ConditionalLeastSquaresEstimation

Parameter

Estimate

StandardError

T-Value

Approx

Pr>|t|

Lag

MU

2.47236

0.21209

11.66

<.0001

0

AR（1,1）

1.00000

0.04125

24.25

<.0001

1

1.11E-6

0.044984

0.212094

-3.37869

-1.38722

20

ConstantEstimateVarianeeEstimateStdErrorEstimateAICSBC

NumberofResiduals

TheMA

（1）modelparametersandAIC,SBC:

Tabie5ConditionalLeastSquaresEstimation

Parameter

Estimate

StandardError

T-Value

Approx

Pr>|t|

Lag

MU

3.34510

0.18211

18.37

<.0001

0

MA（1,1）

-0.85777

0.12761

-6.72

<.0001

1

Table6theMAinformationofAICandBIC

ConstantEstimate

3.345103

Varianee