Title stata.com arch — Autoregressive conditional ...

1 Autoregressive conditional heteroskedasticity (ARCH) family of estimatorsSyntaxMenuDescriptionOptionsRe marks and examplesStored resultsMethods and formulasReferencesAlso seeSyntaxarchdepvar[indepvars] [if] [in] [weight] [,options]optionsDescriptionModelnoconst antsuppress constant termarch(numlist)ARCH termsgarch(numlist)GARCH termssaarch(numlist)simple asymmetricARCH termstarch(numlist)thresholdARCH termsaarch(numlist)asymmetricARCH termsnarch(numlist)nonlinearARCH termsnarchk(numlist)nonlinearARCH terms with single shiftabarch(numlist)absolute valueARCH termsatarch(numlist)absolute thresholdARCH termssdgarch(numlist)lags of tearch(numlist)news terms in Nelson s (1991)EGARCH modelegarch(numlist)lags of ln( 2t)parch(numlist)powerARCH termstparch(numlist)threshold powerARCH termsaparch(numlist)asymmetric powerARCH termsnparch(numlist)nonlinear powerARCH termsnparchk(numlist)nonlinear powerARCH terms with single shiftpgarch(numlist)powerGARCH termsconstraints(constraints)

2 Apply specified linear constraintscollinearkeep collinear variablesModel 2archmincludeARCH-in-mean term in the mean-equation specificationarchmlags(numlist)include specified lags of conditional variance in mean equationarchmexp(exp)apply transformation inexpto anyARCH-in-mean termsarima(#p,#d,#q)specifyARIMA(p,d,q)m odel for dependent variablear(numlist) Autoregressive terms of the structural model disturbancema(numlist)moving-average terms of the structural model disturbancesModel 3distribution(dist[#])usedistdistributio n for errors (may begaussian,normal,t,orged; default isgaussian)het(varlist)includevarlistin the specification of the conditional variancesavespaceconserve memory during estimation12 arch Autoregressive conditional heteroskedasticity (ARCH) family of estimatorsPrimingarch0(xb)compute priming values on the basis of the expected unconditionalvariance.

3 The defaultarch0(xb0)compute priming values on the basis of the estimated variance of theresiduals fromOLSarch0(xbwt)compute priming values on the basis of the weighted sum of squaresfromOLSresidualsarch0(xb0wt)compu te priming values on the basis of the weighted sum of squaresfromOLSresiduals, with more weight at earlier timesarch0(zero)set priming values ofARCH terms to zeroarch0(#)set priming values ofARCH terms to#arma0(zero)set all priming values ofARMA terms to zero; the defaultarma0(p)begin estimation after observationp, wherepis themaximumARlag in modelarma0(q)begin estimation after observationq, whereqis themaximumMAlag in modelarma0(pq)begin estimation after observation (p+q)arma0(#)set priming values ofARMA terms to#condobs(#)set conditioning observations at the start of the sample to#SE/Robustvce(vcetype)vcetypemay beopg,robust, oroimReportinglevel(#)set confidence level.

4 Default islevel(95)detailreport list of gaps in time seriesnocnsreportdo not display constraintsdisplayoptionscontrol column formats, row spacing, and line widthMaximizationmaximizeoptionscontrol the maximization process; seldom usedcoeflegenddisplay legend instead of statisticsYou musttssetyour data before usingarch; see [TS] contain time-series operators; see[U] Time-series ,fp,rolling,statsby, andxiare allowed; see[U] Prefix are allowed; see[U] not appear in the dialog [U] 20 Estimation and postestimation commandsfor more capabilities of estimation fit anARCH(#m)model with Gaussian errors, type.

5 , arch(1/#m)To fit aGARCH(#m,#k)model assuming that the errors follow Student stdistribution with 7 degreesof freedom, type. , arch(1/#m) garch(1/#k) distribution(t 7)You can also fit many other Autoregressive conditional heteroskedasticity (ARCH) family of estimators 3 Details of syntaxThe basic modelarchfits isyt=xt + tVar( t) = 2t= 0+A( , ) +B( , )2(1)Theytequation may optionally includeARCH-in-mean andARMA terms:yt=xt + i ig( 2t i) +ARMA(p,q) + tIf no options are specified,A() =B() =0, and the model collapses to linear regression. Thefollowing options add toA()( , , and represent parameters to be estimated):OptionTerms added toA()arch()A() =A()+ 1,1 2t 1+ 1,2 2t 2+ garch()A() =A()+ 2,1 2t 1+ 2,2 2t 2+ saarch()A() =A()+ 3,1 t 1+ 3,2 t 2+ tarch()A() =A()+ 4,1 2t 1( t 1>0) + 4,2 2t 2( t 2>0) + aarch()A() =A()+ 5,1(| t 1|+ 5,1 t 1)2+ 5,2(| t 2|+ 5,2 t 2)2+ narch()A() =A()+ 6,1( t 1 6,1)2+ 6,2( t 2 6,2)2+ narchk()A() =A()+ 7,1( t 1 7)2+ 7,2( t 2 7)2+ The following options add toB().

6 OptionTerms added toB()abarch()B() =B()+ 8,1| t 1|+ 8,2| t 2|+ atarch()B() =B()+ 9,1| t 1|( t 1>0) + 9,2| t 2|( t 2>0) + sdgarch()B() =B()+ 10,1 t 1+ 10,2 t 2+ Each option requires anumlistargument (see[U] numlist), which determines the laggedterms (1)specifies 1,1 2t 1,arch(2)specifies 1,2 2t 2,arch(1,2)specifies 1,1 2t 1+ 1,2 2t 2,arch(1/3)specifies 1,1 2t 1+ 1,2 2t 2+ 1,3 2t 3, theearch()oregarch()option is specified, the basic model fit isyt=xt + i ig( 2t i) +ARMA(p,q) + tlnVar( t) =ln 2t= 0+C(ln ,z) +A( , ) +B( , )2(2)wherezt= t/ ()andB()are given as above, butA()andB()now add to ln 2trather than 2t.

7 (The options corresponding toA()andB()are rarely specified here.)C()is given by4 arch Autoregressive conditional heteroskedasticity (ARCH) family of estimatorsOptionTerms added toC()earch()C() =C() + 11,1zt 1+ 11,1(|zt 1| 2/ )+ 11,2zt 2+ 11,2(|zt 2| 2/ ) + egarch()C() =C() + 12,1ln 2t 1+ 12,2ln 2t 2+ Instead, if theparch(),tparch(),aparch(),nparch(),np archk(), orpgarch()options arespecified, the basic model fit isyt=xt + i ig( 2t i) +ARMA(p,q) + t{Var( t)} /2= t= 0+D( , ) +A( , ) +B( , )2(3)where is a parameter to be ()andB()are given as above, butA()andB()now addto t.

8 (The options corresponding toA()andB()are rarely specified here.)D()is given byOptionTerms added toD()parch()D() =D()+ 13,1 t 1+ 13,2 t 2+ tparch()D() =D()+ 14,1 t 1( t 1>0) + 14,2 t 2( t 2>0) + aparch()D() =D()+ 15,1(| t 1|+ 15,1 t 1) + 15,2(| t 2|+ 15,2 t 2) + nparch()D() =D()+ 16,1| t 1 16,1| + 16,2| t 2 16,2| + nparchk()D() =D()+ 17,1| t 1 17| + 17,2| t 2 17| + pgarch()D() =D()+ 18,1 t 1+ 18,2 t 2+ Common modelsCommon termOptions to specifyARCH (Engle 1982)arch()GARCH (Bollerslev 1986)arch() garch()ARCH-in-mean (Engle, Lilien, and Robins 1987)archm arch()[garch()]GARCH with ARMA termsarch()

9 Garch() ar() ma()EGARCH (Nelson 1991)earch() egarch()TARCH, threshold ARCH (Zakoian 1994)abarch() atarch() sdgarch()GJR, form of threshold ARCH (Glosten, Jagannathan, and Runkle 1993)arch() tarch()[garch()]SAARCH, simple asymmetric ARCH (Engle 1990)arch() saarch()[garch()]PARCH, power ARCH (Higgins and Bera 1992)parch()[pgarch()]NARCH, nonlinear ARCH narch()[garch()]NARCHK, nonlinear ARCH with one shiftnarchk()[garch()]A-PARCH, asymmetric power ARCH (Ding, Granger, and Engle 1993)aparch()[pgarch()]NPARCH, nonlinear power ARCH nparch()[pgarch()]arch Autoregressive conditional heteroskedasticity (ARCH) family of estimators 5In all cases, you typearchdepvar[indepvars],optionswhereop tionsare chosen from the table above.

10 Each option requires that you specify as its argumentanumlistthat specifies the lags to be included. For mostARCH models, that value will be1. Forinstance, to fit the classic first-orderGARCH model oncpi, you would type. arch cpi, arch(1) garch(1)If you wanted to fit a first-orderGARCH model ofcpionwage, you would type. arch cpi wage, arch(1) garch(1)If, for any of the options, you want first- and second-order terms, specifyoptionname(1/2). Specifyinggarch(1) arch(1/2)would fit aGARCH model with first- and second-orderARCH terms. If youspecifiedarch(2), only the lag 2 term would be arch Autoregressive conditional heteroskedasticity (ARCH) family of estimatorsReading arch outputThe regression table reported byarchwhen using the normal distribution for the errors will Std.