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111JOURNALOFHOUSINGSTUDIES,VOLUME17NO.2,DECEMBER2008*E-mail:ictsai@nuk.edu.twAssistantProfessor,DepartmentofFinance,NationalUniversityofKaohsiung.**E-mail:mcchen@finance.nsysu.edu.twAssociateProfessor,DepartmentofFinance,NationalSunYat-senUniversity.(本文於2007年5月23日收稿，2007年8月27日審查通過，實際出版日期2008年12月)AnAnalysisoftheAsymmetricVolatilityofRealEstatePriceintheTaipeiArea***I-ChunTsai*,Ming-ChiChen**摘 要19732005(leverageeffect)T-GARCH關鍵詞：不動產價格、波動性、抗跌性、不對稱性、T-GARCHABSTRACTAlthoughseveralarticleshavedocumentedthatthereareheteroskedasticautocorrelationsinthevolatilityofrealestateprices,fewofthesepapersdepictoneofthemostcommonlyknownadvantagesofthehousingmarket,namely,itsabilitytobedefensivefromtheviewpointofvola-tilebehavior.Therefore,thisresearchseekstoexamine“defensiveness”inthehousingmarketbyprovidingevidencetoshowtheasymmetricvolatilitybetweenhousepricesmovingupanddown.First,weusethehousepricedataforTaipeifromthesecondquarterof1973tothesecondquarterof2005,andselectthemostsuitablemeanandvarianceequationstoestimatethecondi-tionalheteroskedasticityvolatilityofthereturnonhouseprices.Furthermore,theleverageeffectofthevolatilityvariableisincludedinthemodel,i.e.,T-GARCH(theAsymmetricAutoregres-siveThresholdGARCH)andthenadopted.Theresultoftheempiricaltestshowsthatthereareantileverageeffectsinthevolatilityofthehousingmarket.Therefore,whilethelaggedinnovationsarenegativelycorrelatedwiththehousingreturn,thecurrentvolatilityofthehousingreturnmightde-cline.Theseresultsdepicttheasymmetricvolatilitybetweenhousepricesmovingupanddown,andshowthatthereisadefensiveeffectintheTaipeihousingmarketduringthedataperiodsexamined.Keywords:realestateprice,volatility,defensive,asymmetric,T-GARCH2()Hendry(1984)Meen(1990)Hendry(1984)Giussani&Hadjimatheou(1991)(2007)(leverageeffect)Black(1976)(2007)2006(1)(Autoregres-siveConditionalHeteroscedasticity)T-GARCH(AsymmetricAutoregressiveThresholdGARCH)“”ARCHT-GARCH3(一)不動產市場波動性的估計模型：ARCH與GARCH模型Engle(1982)(AutoregressiveConditionalHeteroscedasticitymodel,ARCHmodel)qBollerslev(1986)ARCH(GeneralizedAutoregressiveConditionalHeteroscedasticitymodel,GARCHmodel)1.ARCHmodelyt(first-orderautoregression)εtARCH(q)yta0a1yt-1εtεtΩt-1~N(0,ht)htω0αiε2t-iht()2.GARCHmodelεtGARCH(p,q)htω0βiht-iαiε2t-iht(二)不動產市場是否存在波動性的不對稱：T-GARCH模型iαiZakoian(1994)T-GARCH()ytεtT-GARCH(p,q)yta0a1yt-1εtεtΩt-1~N(0,ht)htω0βiht-iαiε2t-iγε2t-1Dt-1Dt-1εt-10Dt-11εt-1≥0Dt-10ht4γγγGARCHγγBlack(1976)γγγ(一)資料來源19721999(2)(3)200519732005(二)資料之簡單統計量與單根檢定AugmentedDickey-Fuller(ADF)Phillips-Perron(PP)1I(1)ADFPP5表一 資料之簡單統計量與單根檢定lnPh4.99130.6148-0.28651.3111ADFtest-1.3660PPtest-1.1713ADFtest-8.1494PPtest-8.80351(lineartrend)SIC231%5%10%-3.48-2.88-2.58圖一 價格之時間序列圖6AIC(AkaikeInformationCriterion)SBC(SchwartzBayesianCriterion)表二 平均數迴歸式(AR模型)的決定AR(1)AR(2)AR(3)AR(4)AIC-3.0775-3.0570-3.1870-3.2033SBC-3.0327-2.9894-3.0966-3.0896AR(1)AR(2)AR(1)ARCHAR(1)Engle(1982)LMARCH表三 ARCH效果檢定(TR2)4.31505.50733.855020.730P-value0.03780.06370.27760.0004AR(1)ARCHARCHAR(1)-ARCH(1)AR(1)-ARCH(2)AR(1)-GARCH(1,1)α1(α2)(β1)AR(1)(Loglikelihood)AICSBCR2GARCH(1,1)ARCH(2)R2AICSBCGARCH(1,1)ARCH(1)QGARCH(1,1)(whitenoise)GARCH(1,1)7GARCH(1,1)T-GARCHγ0-0.450.45表四 ARCH與GARCH模型的估計結果ytyta0a1yt-1εtεtt-1~N(0,ht)htω0βiht-iαiε2t-iARCH(1)ARCH(2)GARCH(1,1)a00.00600.0046-0.00210.00340.00120.0036a10.09620.08400.05460.09270.05530.1104ω00.0015*0.00020.0006*0.00020.00020.0001α10.5558*0.14240.2934*0.11720.3014*0.1149α20.6950*0.2316β10.6169*0.1226p-valuep-valuep-valueQ(20)37.640.0130.990.0529.730.07Q2(20)13.740.849.660.9714.910.73AIC-3.1276-3.2946-3.2929SBC-3.0381-3.1826-3.1809R20.0473-0.02110.0039Loglikelihood202.61214.21214.10*0.05Q208(1)(2)圖二 房價報酬與GARCH(1,1)模型之條件變異數序列AICSBCR2T-GARCHGARCHT-GARCHT-GARCH“”9表五 T-GARCH模型的估計結果yta0a1yt-1εtεtΩt-1~N(0,ht)htω0βiht-iαiε2t-iγε2t-1Dt-1Dt-1εt-10Dt-11；εt-1≥0Dt-10T-GARCH(1,1)a00.00390.0035a10.03190.1176ω00.0003*0.0001α10.4337*0.1702β10.6381*0.1051γ-0.4494*0.1879p-valueQ(20)29.770.07Q2(20)16.120.71AIC-3.3414SBC-3.2070R20.0042Loglikelihood218.18*0.05Q2010112122(1999)3Chen&Patel(2002)112007〈2007年2007〈10(2)45-66Black,F.1976“StudiesofStockPriceVolatilityChanges,”Proceedingofthe1976MeetingsoftheBusinessandEconomicsStatisticsSection.AmericanStatisticalAssociation.177-181.Bollerslev,T.1986“GeneralizedAutoregressiveConditionalHeteroskedasticity,”JournalofEconometrics.31:307-328.Chen,M.C.&K.Patel2002“AnEmpiricalAnalysisofDeterminationofHousePricesintheTaipeiArea,”TaiwanEconomicReview.30(4):563-595.Engle,R.F.1982“AutoregressiveConditionalHeteroscedasticitywithEstimatesoftheVarianceofUnit-edKingdomInflation,”Econometrica.50:987-1007.Giussani,B.&G.Hadjimatheou1990“HousePrices:AnEconometricsModelfortheUK,”TheAPEXCentreEconomicsDis-cussionPaper.90/1.Hendry,D.F.1984“EconometricModellingofHousePricesintheUK,”inEconometricsandQuantitativeEconomics.135-172.ed.D.F.Hendry&K.F.Wallis,Oxford:BasilBlackwell.Meen,G.P.1990“TheRemovalofMortgageMarketConstraintsandtheImplicationsforEconometricModellingofUKHousePrices,”OxfordBulletinEconomicsandStatistics.52(1):1-23.Zakoian,J.M.1994“ThresholdHeterosked