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IntheTimeunitanddisplayformatforthetimevariable sectionselecttheformatofthedata,whichinourcasewouldbeYearly.ThenclickeitherSubmitorOKbuttontocompletethecommand.

Thiswholeprocesscanalsobeperformedusingthecommandinterface.Writetssetyear,yearlyinthe

commandwindowforthepresentcase.Ifforexample,indatathetimevariableisdefinedastimeand

the format is monthly, then all one need to write in the command window is tsset time, monthly

Similarlyhaditbeaquarterlydatarequiredtowritetssettime,quarterly.Thefollowingoutputwillbe

displayed:

.tssetyear,yearly

timevariable:year,1981to2004

delta:1year

Timeseriesplotofvariables

Thefirstthingoneshoulddointimeseriesanalysisisgetaviewofthetimeseriesplotofallthevariables

intheanalysis.ToseeaplotofavariablegotoGraphics>>Time-seriesgraphs>>Lineplots.Forthetime

beingconcentrateonlyonthePlotstabonthepopped-upcommandwindow.ClickontheCreatebutton

toseeanotherpopped-upcommandwindow.IntheMaintabselecttheTime-seriesplotintheChoosea

plotcategoryandtypesectionandintheSelecttypedrop-downmenuselectLine.IntheYvariabledrop-

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downmenuselectthevariabletoplotagainsttime.Forexampleselecttheconvariableinourdata

andthenselectthe Submitbutton.Itmaytakefewsecondstoviewtheplotofthevariable.Theplotof

theconvariableinourcaselookslikethefollowing:

Figure:Lineplot

Thisgraph can alsobegenerated usingthe command interface bywriting twoway(tsline con)inthe

command window. One can either select Scatter in the Select type drop-down menu or use the

command interface and write twoway (tsline con, recast(scatter)). The command for line connected

scatterplotistwoway(tslinecon,recast(connected)).

Figure:Scatterplot Figure:Lineconnectedscatterplot

Similargraphsofothervariablescanalsobegeneratedusingthesamecommand.Forexample,forthe

variablergdppcusethecommandof twoway(tsline rgdppc)forlineplotor twoway(tsline rgdppc,

recast(connected))forlineconnectedscatterplot.SavethegraphsusingtheSavegraphbuttononthegraphwindowinthedesiredfolder.

Unit-roottestingforsinglevariable

Mostofthetimeseriesvariablesarenon-stationary.Tocheckfortheunit-rootinthevariablesthereare

manyalternatives.However,themostrecommendedmethodsaretheAugmentedDickey-Fuller(ADF

testandthePhillips-Perron(P-P)test.ToperformtheADFtestgotoStatistics>>Timeseries>>Tests>>

AugmentedDickey-Fullerunit-roottest.IntheMaintabofthepopped-upwindowselectthevariableto

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testfromthedrop-downmenuof Variable.InthesectionofOptionscheckthedesiredboxestohavein

the test.For example, ina single variableunit-root testing the box ofSuppress constant term in the

regressionshouldnotbechecked.Ontheotherhand,theinclusionoftrendand/ordriftterminthe

regressiondependsonthenatureoftheplotofthevariable.Selectthenumberoflagstoincludethe

testfromtheLaggeddifferencestab.Therearenocertainrulestoselectthenumberoflags.OnecanuseAkaike'sinformationcriterion(AIC)orSchwarzBayesianinformationcriteriontodeterminethenumber

oflags.ThereisaruleofthumbthatmanyEconometriciansuseindetermininglags,whichstatesthatif

thedataisyearlythenuseonlyonelag;ifthedataisquarterly,thenuseatleast4lags,andsimilarlyi

thedataismonthly,useupto12lags.Inthisguidetestforunit-rootinthevariableofcon,onelaghas

beenused.Theoutputintheresultwindowlookslikethefollowing:

Wecanaccomplishthesametaskusingthecommandwindow byusing the commandofdfuller con

regresslags(1),whichismucheasiertouse.

TodothePhillips-Perron(P-P)testgotoStatistics>>Timeseries>>Tests>>Phillips-Perronunitroots

test.IntheMaintabselectconintheVariable:drop-downmenuandselectthe defaultlagsoption

andthenpressthesubmitbutton.Insteadofthisusethecommandofpperroncontodothesamething

Theresultwouldlooklikethefollowing:

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Usingthestepsdescribedonecandotheunit-roottestforallthevariablesinthemodelofanalysis.One

pointshouldbenotedisthattheplotofavariablegivesacluewhethertoincludeatrendintotheunit-

roottest.Forexample,theplotofrealGDPpercapitaisgivenbelow.

Theplotclearlyshowsthatthevariablehasabuilt-intrend.So,oneshouldincludethetrendintothe

test.Inourdataforthevariablergdppc,theoptimaltestresultcomesupwithatrendandwith4lags

intotheADFtest.Thecommandforthetestisdfullerrgdppc,trendregresslags(4).FortheP-Ptestthe

commandispperronrgdppc,trend.

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TheresultsshowthatthefirstdifferenceofconisstationaryastheADFteststatistic(-3.093)isgreate

thanthe5%criticalvalue(-3.000)inabsolutetermsand/ortheMackinnonp-valueoftheP-Pstatisticis

approximatelyzero.Similarly,usethesamemethodtoshowthatalltheothervariablesarestationaryin

thefirstdifferencedform.So,thevariablesareintegratedoforderone {I(1)}.Remembertoincludea

trendtermintotheunit-roottestofthedrgdppcvariable.

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Testingforcointegrationin{I(1)}variables:ErrorCorrectionModel(ECM)

Using the data one can estimate a linear demand function of cigarettes. In estimating the demand

functionwithtimeseriesdata,theestimationmethodologyisverycrucial(seeforinstanceHarris,1995)

Themajorconcernwiththetimeseriesisthatifnon-stationarityofdataseriespersiststhenitmayleadtospuriousrelationship.Toavoidthisproblem,itisnecessarytousethecointegrationmethodology.The

regressionequationcanbeestimatedfortheperiodof1981to2004usingtheEngel-Granger(E-G)two-

step procedure (Engel and Granger, 1987). The first step is to estimate a long-run equation using

ordinaryleastsquares(OLS)withvariables,whichareintegratedoforderone, I(1),intheirlevels.In

ordertoavoidspuriousregression,residualbasedcointegrationtestcanbeused,wherethestationarity

oftheresidualimpliesaconintegratingrelationshipamongthevariablesinthelongrunequation.The

secondstepoftheE-Gprocedureistoestimatethecorrespondingerror-correctionmodel(ECM),based

onthelongruncointegratingrelationshiptoobservetheshortrundynamics(EngelandGranger,1987).

OnecanestimateanECMusingtheresidualfromthelong-runequation.TheECMisbasedonstationary

data(asalltheI(1)regressorsareinfirstdifferenceform)andincludesthelaggedresidualsofthelongrunequation,whichisalsoI(0)whenthevariableshavecointegratingrelationship.Onethingyoushould

know is that the dummy variables are not continuous. As a result, you need not worry about the

stationarityofthedummyvariables.Thetwodummyvariablesfortheyearof1993and1995arehereto

controlfortheunusualtroughandspikesrespectivelyintheconsumptiondata.

ThefirststepoftheE-GistorunanOLSregressiononthevariablesintheirlevels.Thecommandforthe

regressionisregconrelprcrgdppcdum93dum95.

Togettheresidualfromthisregressionwecanusethecommandof predictresid,r,whereresidisthe

variablenameofthepredictedresidual.Theunit-rootoftheresidualcanbetestedbyADFand/orP-P

test.However,onemustrememberthatinthiscaseyouhavetocheckforthenoconstantterminthe

regressionoptionandthecriticalvaluesshouldbecalculatedusingtheMacKinnonsresponsesurface

analysistable(Mackinnon,1991).ThecommandfortheADFtestforresidualis dfullerresid,noconstant

regresslags(3)andfortheP-Ptestispperronresid,noconstantregress.

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The MacKinnon critical values for the cointegrating equation of 3 variables without trend using 24

observations at1%,5%and 10% levelofsignificance are -4.954, -4.114, and -3.717 respectively. The

Dickey-Fuller critical values for this regression at 1%, 5%, and 10% level are -2.66, -1.95, and -1.60

respectively.So,onecanclearlyseethattheMacKinnoncriticalvaluesaremuchhigherthantheDickey-

Fullercriticalvalues.AsaresultusingtheD-Fcriticalvaluescanleadtoerrorinstatisticalanalysis.

OnecanseethattheADFteststatistic(-2.947)islowerthantheMacKinnoncriticalvalueevenat10%level.So,usingADFtestonecannotsaythattheresidualfromtheregressionisstationary.However,the

P-Pteststatistic(-4.406)ishigherthantheMacKinnoncriticalvalueat5%level.So,itshowsthatthe

residual is stationary.Considering the fact that asDittmann(2002) argued,Phillips-Perrontest when

appliedtoresidualbasedconintegrationdeterminationaremorepowerfulthantheADFtest,onecan

arguethatthereexistsacointegratingrelationshipinthelong-rundemandequationofcigarettes.

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Onecanrunashortrunerrorcorrectionmodel(ECM).IntheECM,theoneperiodlaggedresidualfor

annualdataactsastheerrorcorrectionterm.Toget theoneperiod lagged residualonecanuse the

commandasgenlagresid=resid[_n-1].

ThecommandfortheECMinthiscaseisregdcondrelprcdrgdppcddum93ddum95lagresid.

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References:

IngolfDittmann(2002):Residual-BasedTestsforFractionalCointegration:AMonteCarloStudy,Journal

ofTimeSeriesAnalysis,Volume21Issue6,Pages615647.

JamesMacKinnon(1991):CriticalValuesforCointegrstionTests,inR.EngelandC.Granger,Long-run

EconomicRelationships,OxfordUniversityPress.Richard I. D. Harris (1995): Using Cointegration analysis in Econometric Modelling, FT Prentice Hal

Publication.

RobertAngelandCliveGranger(1987):Cointegrationanderrorcorrection:Representation,estimatio

andtesting,Econometrica,55:251-276.

Appendix:Thedatasetusedforthistutorial:

year con relprc rgdppc dum93 dum95 trend

1981 754.15 12.54 10273.60 0 0 1

1982 788.90 13.59 10322.57 0 0 2

1983 701.55 13.24 10518.93 0 0 3

1984 735.55 14.83 10832.18 0 0 4

1985 719.65 15.30 10951.98 0 0 5

1986 718.25 15.91 11199.04 0 0 6

1987 738.10 16.47 11376.67 0 0 7

1988 701.55 17.27 11408.75 0 0 8

1989 704.40 16.20 11473.76 0 0 9

1990 614.45 19.83 11797.61 0 0 10

1991 680.20 17.89 11938.95 0 0 11

1992 625.80 16.76 12286.00 0 0 12

1993 575.80 17.34 12724.48 1 0 13

1994 632.75 17.20 12994.34 0 0 14

1995 868.95 16.10 13381.83 0 1 15

1996 811.10 15.36 13768.54 0 0 16

1997 930.05 14.69 14297.28 0 0 17

1998 994.45 15.49 14815.08 0 0 18

1999 977.90 16.66 15315.05 0 0 19

2000 986.60 15.74 15997.47 0 0 20

2001 1006.00 15.59 16607.80 0 0 21

2002 1019.20 15.08 17117.09 0 0 22

2003 1124.95 14.70 17773.69 0 0 23

2004 1151.25 14.06 18504.51 0 0 24

Note:

Thetheoreticalpremiseandmethodologyusedinthistutorialisforillustrativepurposesonly.

AdditionalResources

QuestionspertainingtoStata-10forTimeSeriesAnalysiscanbesubmittedtoNYUsDataServiceStudio

atdata.service@nyu.edu.