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1、VolatilityandARCH/GARCHModels: AReviewReferencesTheclassics:•Engle,R.F.(1982),AutoregressiveConditionalHeteroskedasticitywithEstimatesoftheVarianceofU.K,Econometrica.•Bollerslev,T.P.(1986),GeneralizedAutoregresiveConditionalHeteroscedasticity,JournalofEconometrics.Introduction/R
2、eviews:•BollerslevT.,EngleR.F.andD.B.Nelson(1994),ARCHModels,HandbookofEconometricsVol.4.•Engle,R.F.(2001),GARCH101:TheUseofARCH/GARCHModelsinAppliedEconometrics,JournalofEconomicPerspectives.•Untiltheearly1980seconometricshadfocusedalmostsolelyonmodelingthemeansofseries-i.e.,th
3、eiractualvalues.yt=Et(yt
4、x)+εt,εt῀D(0,σ2)ForanAR(1)process:Et-1(yt
5、x)=Et-1(yt)=α+βyt-1Note:E(yt)=α/(1-β)andVar(yt)=σ2/(1-β2)Theconditionalfirstmomentistimevarying,thoughtheunconditionalmomentisnot!Keydistinction:Conditionalvs.Unconditionalmoments.•SimilarideaforthevarianceUncond
6、itionalvariance:Var(yt)=E[(yt–E[yt])2]=σ2/(1-β2)Conditionalvariance:Vart-1(yt)=Et-1[(yt–Et-1[yt])2]=Et-1[εt2]Vart-1(yt)isthetruemeasureofuncertaintyattimet-1.meanvarianceConditionalvarianceStylizedFactsofAssetReturnsi)Thicktails-Mandelbrot(1963):leptokurtic(thickerthanNormal)ii)
7、Volatilityclustering-Mandelbrot(1963):“largechangestendtobefollowedbylargechangesofeithersign.”iii)LeverageEffects–Black(1976),Christie(1982):Tendencyforchangesinstockpricestobenegativelycorrelatedwithchangesinvolatility.iv)Non-tradingEffects,WeekendEffects–Fama(1965),FrenchandR
8、oll(1986):Whenamarketisclosedinformationaccumulatesatadifferentratetowhenitisopen–forexample,theweekendeffect,wherestockpricevolatilityonMondayisnotthreetimesthevolatilityonFriday.vi)Volatilityandserialcorrelation–LeBaron(1992):Inverserelationshipbetweenthetwo.vii)Co-movementsin
9、volatility–RamchandandSusmel(1998):Volatilityispositivelycorrelatedacrossmarkets/assets.v)Expectedevents–Cornell(1978),PatellandWolfson(1979),etc:Volatilityishighatregulartimessuchasnewsannouncementsorotherexpectedevents,orevenatcertaintimesofday–forexample,lessvolatileintheearl
10、yafternoon.Figure:DescriptiveStatisticsandDistr
