時間序列分析——VAR模型試驗資料

1、基于VAR模型的我國房地產(chǎn)市場與匯率波動的因果關(guān)系VAR莫型實驗第一部分實驗分析目的及方法現(xiàn)選取人民幣對美元匯率以及商品房房價作為變量構(gòu)建VAF模型。對于不滿足單位根檢驗的序列采取對數(shù)化或差分處理，使其成為平穩(wěn)序列再進行模型的擬合。對于商品房房價這一變量，由于全國各省市差異較大，故此處采用全國房地產(chǎn)開發(fā)業(yè)綜合景氣指數(shù)這一變量。此外，為了消除春節(jié)假期不固定因素帶來的影響，增強數(shù)據(jù)的可比性，按照國家統(tǒng)計制度，從2012年起，不單彳對1月份統(tǒng)計數(shù)據(jù)進行調(diào)查，1-2月份數(shù)據(jù)一起調(diào)查，一起發(fā)布。所以國房景氣指數(shù)p這一序列缺少每年一月份的相關(guān)數(shù)據(jù)，屬于非隨機、不可忽略缺失，在此采用平均值填充的方法，補足數(shù)

2、據(jù)。第二部分實驗樣本2.1 數(shù)據(jù)來源數(shù)據(jù)來源于中經(jīng)網(wǎng)統(tǒng)計數(shù)據(jù)庫。具體數(shù)據(jù)見附錄表。2.2 所選數(shù)據(jù)變量由于我國于2005年7月實行第二次匯改，此次匯改以市場供求為基礎(chǔ)、參考一P!4T子貨幣進行調(diào)節(jié)、有管理的浮動匯率制度取代了過去人民幣匯率長達10年的緊盯美元的固定匯率體制。故本實驗擬選取2005年07月到2014年10月我國以月為單位的數(shù)據(jù)。用以上兩個變量來構(gòu)建VAR模型，并利用該模型進行分析預(yù)測。第四部分模型構(gòu)建4.1 判斷序列的平穩(wěn)性4.1.1 匯率E序列首先繪制出E的折線圖，結(jié)果如下圖:圖4.1匯率E的曲線圖從圖中可以看出，匯率E序列較強的趨勢性，由此可以初步判斷該序列是非平穩(wěn)的。為了減

3、少m的變動趨勢以及異方差性，先對m進行對數(shù)化處理，記為lm,其時序圖如下:圖4.2lm的曲線圖對數(shù)化后的趨勢性減弱，但仍存在一定的趨勢性，下面對lm進行一階差分處理，去除趨勢性，得到新變量dlm,觀察dlm的曲線圖。DLE圖4.3DLE的曲線圖從圖中可以看出，dle序列的趨勢性基本已經(jīng)消除，且新變量dle基本圍繞0上下波動,因此選擇形式為yt=yt-i+ut進行單位根檢驗：表4.1單位根輸出結(jié)果NullHypothesis:DLEhasaunitrootExogenous:ConstantLagLength:2(Automatic-basedonSIC,maxlag=12)t-Statisti

4、cProb.MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(DLE)Method:LeastSquaresDate:11/15/14Time:20:20Sample(adjusted):2005M112014M10Includedobservations:108afteradjustments4AugmentedDickey-Fullerteststatistic-3.0316730.0351Testcriticalvalues:1%level-3.4919285%le

5、vel-2.88841110%level-2.581176VariableCoefficientStd.Errort-StatisticProb.DLE(-1)-0.3530050.116439-3.0316730.0031D(DLE(-1)-0.5027300.115417-4.3557680.0000D(DLE(-2)-0.3115310.093265-3.3402580.0012C-0.0008880.000470-1.8875920.0619R-squared0.450240Meandependentvar1.15E-05AdjustedR-squared0.434382S.D.dep

6、endentvar0.005058S.E.ofregression0.003804Akaikeinfocriterion-8.269046Sumsquaredresid0.001505Schwarzcriterion-8.169708Loglikelihood450.5285Hannan-Quinncriter.-8.228768F-statistic28.39119Durbin-Watsonstat2.061613Prob(F-statistic)0.000000單位根統(tǒng)計量ADF=3.031673小于臨界值，且P為0.0351,因此該序列不是單位根過程,即該序列是平穩(wěn)序列。4.1.2 國房

7、景氣指數(shù)P序列首先作出P序列的時序圖：圖4.4P的曲線圖由于每年一月份的數(shù)據(jù)缺失，故取相鄰兩項進行平均補全數(shù)據(jù)，得到新序列的時序圖如下:由上圖可知，該序列P可能存在一定的趨勢性和季節(jié)性，先進行單位根檢驗，確定改序列是否平穩(wěn)。由于序列表4.2單位根輸出結(jié)果NullHypothesis:PhasaunitrootExogenous:Constant,LinearTrendLagLength:3(Automatic-basedonSIC,maxlag=12)t-StatisticProb.*AugmentedDickey-Fullerteststatistic-3.9724570.0124Testc

8、riticalvalues:1%level-4.0452365%level-3.45195910%level-3.151440*MacKinnon(1996)one-sidedp-values.由單位根檢驗結(jié)果可知，T值小于臨界值，且P=0.0124,在5%勺置信水平下，該序列不存在單位根過程。由于匯率E序列為一階單整序列，并進行了一階差分處理，因此樣本數(shù)量減少，在下面的操作中，所有的樣本序列調(diào)整為2005-08至2014-10。4.2 模型參數(shù)識別先進行VAR模型的擬合，初步選定滯后階數(shù)為3:表4.3擬合輸出結(jié)果VectorAutoregressionEstimatesDate:11/22/

9、14Time:22:20Sample(adjusted):2005M112014M10Includedobservations:108afteradjustmentsStandarderrorsin()&t-statisticsinDLEPDLE(-1)0.063183-19.12274(0.09626)(14.1374)0.65638-1.35263DLE(-2)0.11679815.42129(0.09604)(14.1052)1.216151.09330DLE(-3)0.24526016.39171(0.09617)(14.1243)2.550301.16053P(-1)-9.0

10、4E-051.490708(0.00066)(0.09765)-0.1359315.2656P(-2)-0.000583-0.355442(0.00118)(0.17380)-0.49226-2.04508P(-3)0.000346-0.160740(0.00067)(0.09872)0.51479-1.62821C0.0313282.571540(0.01274)(1.87084)2.459431.37454R-squared0.2950330.979509Adj.R-squared0.2531540.978292Sumsq.resids0.00139029.99247S.E.equatio

11、n0.0037100.544936F-statistic7.044848804.6767Loglikelihood454.8094-84.06138AkaikeAIC-8.2927661.686322SchwarzSC-8.1189241.860164Meandependent-0.002527100.2406S.D.dependent0.0042933.698585Determinantresidcovariance(dofadj.)4.08E-06Determinantresidcovariance3.57E-06Loglikelihood370.8871Akaikeinformation

12、criterion-6.609021Schwarzcriterion-6.261337再進行滯后階數(shù)的確定：表4.4最優(yōu)滯后階數(shù)的判斷VARLagOrderSelectionCriteriaEndogenousvariables:DLEPExogenousvariables:CDate:11/22/14Time:22:22Sample:2005M072014M10Includedobservations:99LagLogLLRFPEAICSCHQ0134.7784NA0.000234-2.682392-2.629965-2.6611801302.5627325.39998.57e-06-5.9

13、91165-5.833886-5.9275302329.023050.247835.45e-06-6.444909-6.182775indicateslagorderselectedbythecriterionLR:sequentialmodifiedLRteststatistic(eachtestat5%level)FPE:FinalpredictionerrorAIC:AkaikeinformationcriterionSC:Schwarzinformationcriterion-6.338849*3334.37339.943949*5.30e-06*-6.472187*-6.105200

14、-6.3237044337.45315.5997425.40e-06-6.453598-5.981758-6.2626915339.75894.0991765.60e-06-6.419372-5.842679-6.1860416345.04989.1923245.46e-06-6.445451-5.763905-6.1696967345.54840.8460765.87e-06-6.374716-5.588316-6.0565378346.73691.9687606.23e-06-6.317917-5.426663-5.9573149352.58019.4436396.01e-06-6.355

15、154-5.359047-5.95212810353.77141.8770826.39e-06-6.298411-5.197451-5.85296111354.36490.9112796.87e-06-6.229594-5.023780-5.74172012356.46173.1346447.18e-06-6.191146-4.880479-5.660848HQ:Hannan-Quinninformationcriterion由上邊可知，根據(jù)信息準則，采取少數(shù)服從多數(shù)原則，取滯后階數(shù)為3,此外取滯后階數(shù)為2(SC為-6.182775)或取滯后階數(shù)為3(SC為-6.105200)時，兩者SC值相

16、差不是很大。3.3模型參數(shù)估計選取了最優(yōu)?t后階數(shù)3,進行模型的擬合。擬合結(jié)果如下:表4.5VAR(3膜型估計結(jié)果VectorAutoregressionEstimatesDate:11/22/14Time:22:23Sample(adjusted):2005M112014M10Includedobservations:108afteradjustmentsStandarderrorsin()&t-statisticsinDLEPDLE(-1)0.063183-19.12274(0.09626)(14.1374)0.65638-1.35263DLE(-2)0.11679815.4212

17、9(0.09604)(14.1052)1.216151.09330DLE(-3)0.24526016.39171(0.09617)(14.1243)2.550301.16053P(-1)-9.04E-051.490708(0.00066)(0.09765)-0.1359315.2656P(-2)-0.000583-0.355442(0.00118)(0.17380)-0.49226-2.04508P(-3)0.000346-0.160740(0.00067)(0.09872)0.51479-1.62821C0.031328(0.01274)2.459432.571540(1.87084)1.3

18、7454R-squared0.2950330.979509Adj.R-squared0.2531540.978292Sumsq.resids0.00139029.99247S.E.equation0.0037100.544936F-statistic7.044848804.6767Loglikelihood454.8094-84.06138AkaikeAIC-8.2927661.686322SchwarzSC-8.1189241.860164Meandependent-0.002527100.2406S.D.dependent0.0042933.698585Determinantresidco

19、variance(dofadj.)4.08E-06Determinantresidcovariance3.57E-06Loglikelihood370.8871Akaikeinformationcriterion-6.609021Schwarzcriterion-6.261337由回歸結(jié)果可知，VAR模型的參數(shù)估計一部分顯著。估計的方程為：DLE=0.0631825185907*DLE(-1)+0.116798166932*DLE(-2)+0.245260334897*DLE(-3)9.03782278173e-05*P(-1)-0.000582535557655*P(-2)+0.000346

20、029705954*P(-3)+0.0313284849005P=-19.1227437147*DLE(-1)+15.421290462*DLE(-2)+16.3917067335*DLE(-3)+1.4907076294*P(-1)-0.355441747867*P(-2)-0.160740461814*P(-3)+2.571539785444.4模型檢驗首先對模型進行平穩(wěn)性檢驗表4.6VAR模型平穩(wěn)性檢驗的表格顯示RootsofCharacteristicPolynomialEndogenousvariables:DLEPExogenousvariables:CLagspecificati

21、on:13Date:11/22/14Time:22:27RootModulus0.883466-0.097039i0.8887790.8887790.883466+0.097039i100.6703000.670300-0.321875-0.501863i0.596213-0.321875+0.501863i0.596213-0.2395920.239592Norootliesoutsidetheunitcircle.VARsatisfiesthestabilitycondition.nverseRootsofARCharacteristicPolynomial1.5100.50.0- 0.5

22、- 1.0- 1.5-15-1.0-0.50.00.51.01.5圖4.6VAR模型平穩(wěn)性檢驗的圖形顯示由上表和上圖可知，VAR模型的特征方程的根均在單位園內(nèi)，因此VAR模型是平穩(wěn)的。卜面進行殘差的自相關(guān)性的檢驗，檢驗結(jié)果如下：11Aulocorrelatioiiswith2Std.Err.BoundsCcrtDLEDLE(-i)CortDLE圖4.7VAR模型各方程殘差項的自相關(guān)圖由上圖可知，VAR模型允許不同方程的殘差之間存在交叉相關(guān)性,但是殘差自身不存在自相關(guān)性，因此，觀察殘差自身的自相關(guān)圖,可以看出自相關(guān)系數(shù)均位于置信區(qū)間內(nèi)，說明殘差不存在自相關(guān)性。第五部分模型應(yīng)用5.1 格蘭杰因果檢

23、驗接下來做兩兩變量之間的格蘭杰因果檢驗。序列P與序列DLE:表5.1序列P與序列DLE格蘭杰因果檢驗表PairwiseGrangerCausalityTestsDate:11/21/14Time:23:32Sample:2005M072014M10Lags:3NullHypothesis:ObsF-StatisticProb.12PdoesnotGrangerCauseDLEDLEdoesnotGrangerCauseP1082.777600.04511.342860.2648由上述結(jié)果可知，在5%勺置信水平下，P是dle的格蘭杰原因，即全國房地產(chǎn)開發(fā)業(yè)綜合景氣指數(shù)是人民幣對美元匯率變動幅度的

24、格蘭杰原因。5.2 脈沖響應(yīng)由于脈沖響應(yīng)函數(shù)收到變量順序的影響，因此其結(jié)果與分析的主觀因素有關(guān)，對于這三個變量：DLERP,按照中國市場目前現(xiàn)狀，認為DLE外生性最強，p其次最后為r。故選取順序為DLEP、RoResponseioCholeskyOn由S.DInnovations?2S.E.ResponseofDLEtoDLE圖5.1脈沖響應(yīng)圖5.3 方差分解表5.4方差分解結(jié)果Variance13DecompositionofDLE:PeriodS.E.DLEP10.003710100.00000.00000020.00371899.982500.01750030.00376998.8931

25、11.10688540.00392997.909522.09048150.00396696.365083.63491860.00401994.218215.78179370.00407892.060357.93964980.00412989.8151510.1848590.00418287.6054512.39455100.00423185.5997514.40025110.00427683.8063816.19362120.00431682.2474817.75252130.00435180.9365819.06342140.00438179.8538420.14616150.0044067

26、8.9772421.02276160.00442678.2831821.71682170.00444277.7439622.25604180.00445477.3334522.66655190.00446477.0279322.97207200.00447176.8058323.19417210.00447676.6485523.35145220.00447976.5405123.45949230.00448276.4688723.53113240.00448376.4233623.57664250.00448476.3960023.60400260.00448576.3807123.6192

27、9270.00448576.3730623.62694280.00448676.3698923.63011290.00448676.3690623.63094300.00448676.3691923.63081310.00448676.3694723.63053320.00448676.3694623.63054330.00448676.3690023.63100340.00448676.3680723.63193350.00448676.3667523.63325360.00448676.3651623.63484VarianceDecom14positionofP:PeriodS.E.DL

28、EP10.5449360.25733799.7426620.9837341.37891298.6210931.4187241.20744898.7925541.8251420.82489299.1751152.1948950.59927299.4007362.5220960.45388299.5461272.8070260.38586299.6141483.0507090.37289099.6271193.2558400.40512599.59488103.4259920.46978699.53021113.5649130.55340199.44660123.6765910.64929299.

29、35071133.7649360.75050199.24950143.8336290.85127199.14873153.8860880.94810499.05190163.9253751.03814598.96186173.9541801.11948298.88052183.9748111.19116998.80883193.9892071.25283598.74717203.9989591.30464098.69536214.0053421.34717398.65283224.0093541.38127898.61872234.0117561.40797098.59203244.01311

30、21.42833898.57166254.0138271.44346398.55654264.0141791.45436298.54564274.0143511.46195298.53805284.0144571.46702898.53297294.0145601.47025498.52975304.0146901.47216798.52783314.0148561.47318898.52681324.0150541.47363598.52636334.0152741.47373998.52626344.0155041.47366298.52634354.0157341.47350998.52

31、649364.0159531.47334998.52665附錄15具體數(shù)據(jù)指標國房景氣指數(shù)當月人民幣對美元期末匯率地區(qū)全國全國頻度月月單位-人民幣/美元2005-07101.978.112005-08101.768.12005-09101.428.092005-10101.028.082005-11100.698.082005-12100.618.072006-01100.768.062006-02101.058.042006-03101.468.022006-04101.618.022006-05101.878.022006-06102.9382006-07103.517.972006-08

32、103.317.962006-09103.147.912006-10103.47.882006-11103.927.842006-12102.967.812007-01102.427.782007-02101.787.742007-03101.227.732007-04102.657.712007-05103.327.652007-06103.637.622007-071047.572007-08104.487.562007-09104.997.512007-10105.747.472007-11106.597.42007-12106.457.32008-01106.117.192008-02

33、105.557.112008-03104.727.022008-04104.0772008-05103.346.942008-06103.086.862008-07102.366.842008-08101.786.832008-09101.156.822008-1099.686.832008-1198.466.832008-1296.466.832009-0195.666.842009-0294.866.842009-0394.746.842009-0494.766.832009-0595.946.832009-0696.556.832009-0798.016.832009-08100.086.832009-09101.086.832009-10102.036.832009-11102.786.832009-12103.666.832010-01104.5656.832010-