时间序列分析var模型实验

基于 VAR 模型的我国房地产市场与汇率 波动的因果关系VAR 模型实验第一部分 实验分析目的及方法现选取人民币对美元汇率以及商品房房价作为变量构建 VAR 模型。对于不满足单位 根检验的序列采取对数化或差分处理， 使其成为平稳序列再进行模型的拟合。对于商品 房房价这一变 量，由于全国各省市差异较大， 故此处采用全国房地产开发业综合景气指 数这一变量。此外，为了消除 春节假期不固定因素带来的影响，增强数据的可比性，按 照国家统计制度， 从 2012 年起，不单独对 1 月份统计数据进行调查， 1-2 月份数据一起 调查，一起发布。所以国房景气指数 p 这一序列缺少每年一 月份的相关数据，属于非随 机、不可忽略缺失，在此采用平均值填充的方法，补足数据。第二部分 实验样本2.1 数据来源数据来源于中经网统计数据库。具体数据见附录表。2.2 所选数据变量由于我国于 2005 年 7月实行第二次汇改，此次汇改以市场供求为基础、 参考一 篮 子货币进行调节、有管理的浮动汇率制度取代了过去人民币汇率长达 10 年的紧盯美元 的固定汇率体制。 故本实验拟选取 2005 年 07月到 2014年 10月我国以月为单位的数据。 用以上两个 变量来构建 VAR 模型，并利用该模型进行分析预测。第四部分 模型构建4.1 判断序列的平稳性4.1.1 汇率 E 序列首先绘制出 E 的折线图，结果如下图：6200520062007 2QQS 20092Q10201120122013 2CU6.BH丁0图4.1汇率E的曲线图从图中可以看出，汇率E序列较强的趋势性，由此可以初步判断该序列是非平稳的。为了减少m的变动趋势以及异方差性，先对m进行对数化处理，记为Im,其时序图如下:LE2C0E 20 兀2007209&200&201320112012201320 2图4.2 Im的曲线图对数化后的趋势性减弱，但仍存在一定的趋势性，下面对Im进行一阶差分处理，去除趋势性，得到新变量dim,观察dim的曲线图。CLE图4.3 DLE的曲线图从图中可以看出，die序列的趋势性基本已经消除，且新变量die基本围绕0上下波动,因此选择形式为yt=yt-i+ut进行单位根检验：表4.1单位根输出结果Null Hypothesis: DLE has a unit rootExogenous: ConstantLag Length: 2 (Automatic - based on SIC, maxlag=12)t-StatisticProb.MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLE) Method: Least SquaresDate: 11/15/14 Time: 20:20Sample (adjusted): 2005M11 2014M10Included observations: 108 after adjustmentsAugme nted Dickey-Fuller test statistic-3.0316730.0351Test critical values:1% level-3.4919285% level-2.88841110% level-2.581176VariableCoefficie ntStd. 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-squared0.450240Mean depe ndent var1.15E-05Adjusted R-squared0.434382S.D.dependent var0.005058S.E. of regressi on0.003804Akaike info criteri on-8.269046Sum squared resid0.001505Schwarz criteri on-8.169708Log likelihood450.5285Hannan-Quinn criter.-8.228768F-statistic28.39119Durbi n-Wats on stat2.061613Prob(F-statistic)0.000000，因此该序列不是单位根过 单位根统计量ADF二-3.031673小于临界值，且P为0.0351程即该序列是平稳序列。4.1.2国房景气指数P序列首先作出P序列的时序图:图4.4 P的曲线图由于每年一月份的数据缺失， 故取相邻两项进行平均补全数据， 得到新序列的时序图如下:1302coe图4.5 P 的Illi线图(补全)p r I 1 11 Mil 11 11 F 1 R c 1 11 I |p V 11 HUMI K III I I T I20Ttii 11 t n | i f r i ii 11 t I n j ii i ri Einn |r r i t p him | i i f i m hi i if | r i r v e iv t ri i 2007200820092M0JF稳。由上图可知，该序列 P 可能存在一定的趋势性和季节性，先进行单位根检验，确定 改序列是否平由于序列表 4.2 单位根输出结果Null Hypothesis: P has a unit rootExogenous: Constant, Linear TrendLag Length: 3 (Automatic - based on SIC, maxlag=12)t-StatisticProb.*Augme nted Dickey-Fuller test statistic-3.9724570.0124Test critical values:1% level-4.0452365% level-3.45195910% level-3.151440*MacKinnon (1996) one-sided p-values.由单位根检验结果可知，T值小于临界值，且P=0.0124,在5%勺置信水平下，该序列不存在单位根过程。由于汇率 E 序列为一阶单整序列,并进行了一阶差分处理,因此样本数量减少,在4.2 模型参数识别先进行VAR模型的拟合，初步选定滞后阶数为3:表 4.3 拟合输出结果Vector Autoregression EstimatesDate: 11/22/14 Time: 22:20Sample (adjusted): 2005M11 2014M10Included observations: 108 after adjustments Standard errors in ( ) & t-statistics in DLEPDLE(-I)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)-9.04E-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)0.51479-1.62821C0.0313282.571540(0.01274)(1.87084)2.459431.37454R-squared0.2950330.979509Adj. R-squared0.2531540.978292Sum sq. resids0.00139029.99247S.E. equati on0.0037100.544936F-statistic7.044848804.6767Log likelihood454.8094-84.06138Akaike AIC-8.2927661.686322Schwarz SC-8.1189241.860164Mean depe ndent-0.002527100.2406S.D.dependent0.0042933.698585Determ inan t resid covaria nee (dof adj.)4.08E-06Determ inant resid covaria nee3.57E-06Log likelihood370.8871Akaike inf ormatio n criteri on-6.609021Schwarz criteri on-6.261337再进行滞后阶数的确定：表 4.4 最优滞后阶数的判断VAR Lag Order Selection Criteria Endogenous variables: DLE P Exogenous variables: C Date: 11/22/14 Time: 22:22Sample: 2005M07 2014M10Included observations: 99LagLogLLRFPEAICSCHQ0134.7784NA0.000234-2.682392-2.629965-2.6611801302.5627325.39998.57e-06-5.991165-5.833886-5.9275302329.023050.247835.45e-06-6.444909-6.182775*-6.338849*3334.37339.943949*5.30e-06*-6.472187*-6.105200-6.3237044337.45315.5997425.40e-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-06-6.355154-5.359047-5.95212810353.77141.8770826.39e-06-6.298411-5.197451-5.85296111354.36490.9112796.87e-06-6.229594-5.023780-5.74172012356.46173.1346447.18e-06-6.191146-4.880479-5.660848* indicates lag order selected by the criterionLR: sequential modified LR test statistic (each test at 5% level)FPE: Final prediction errorAIC: Akaike information criterionSC: Schwarz information criterionHQ: Hannan-Quinn information criterion3,此外取滞SC值相差不是由上边可知，根据信息准则，采取少数服从多数原则，取滞后阶数为后阶数为2(SC为-6.182775 )或取滞后阶数为3(SC为-6.105200 )时，两者很大。3.3模型参数估计选取了最优滞后阶数3,进行模型的拟合。拟合结果如下表4.5 VAR(3)模型估计结果Vector Autoregression EstimatesDate: 11/22/14 Time: 22:23Sample (adjusted): 2005M11 2014M10Included observations: 108 after adjustmentsStandard errors in ( ) & t-statistics in DLEPDLE(-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)-9.04E-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)0.51479-1.62821C0.0313282.571540(0.01274)(1.87084)2.459431.37454R-squared0.2950330.979509Adj. R-squared0.2531540.978292Sum sq. resids0.00139029.99247S.E. equati on0.0037100.544936F-statistic7.044848804.6767Log likelihood454.8094-84.06138Akaike AIC-8.2927661.686322Schwarz SC-8.1189241.860164Mean depe ndent-0.002527100.2406S.D.dependent0.0042933.698585Determi nant resid covaria nee(dof adj.)4.08E-06Determ inant resid covaria nee3.57E-06Log likelihood370.8871Akaike inf ormatio n criteri on-6.609021Schwarz criteri on-6.261337由回归结果可知，VAR模型的参数估计一部分显著。估计的方程为:DLE = 0.0631825185907 * DLE(-1)+ 0.116798166932 * DLE(-2)+ 0.245260334897 * DLE(-3)9.03782278173e-05 * P(-1)- 0.000582535557655 * P(-2)+ 0.000346029705954 * 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模型检验首先对模型进行平稳性检验表4.6 VAR模型平稳性检验的表格显示Roots of Characteristic Polynomial Endogenous variables: DLE P Exogenous variables: CLag specification: 1 3Date: 11/22/14Time: 22:27RootModulus0.883466 -0.097039i0.8887790.883466 + 0.097039i0.8887790.6703000.670300-0.321875-0.501863i0.596213-0.321875+ 0.501863i0.596213-0.2395920.239592No root lies outside the unit circle.VAR satisfies the stability condition.Inverse Roots of AR Characteristic Polynomial图4.6 VAR模型平稳性检验的图形显示因此VAR模型是平稳的。由上表和上图可知，VAR模型的特征方程的根均在单位园内,F面进行残差的自相关性的检验，检验结果如下:Airtocorrelations witti 2 Sfd Frr RoundsCorPfDLE(J1235*BCor(DLE.P(i)?图4.7 VAR模型各方程残差项的自相关图由上图可知，VAR模型允许不同方程的残差之间存在交叉相关性，但是残差自身不存在自相关性,因此，观察残差自身的自相关图，可以看出自相关系数均位于置信区间内，说明残差不存在自相关性。第五部分模型应用5. 1格兰杰因果检验接下来做两两变量之间的格兰杰因果检验。序列P与序列DLE:表5】序列P与序列DLE格兰杰因果检验表Pairwise Granger Causality TestsDate: 11/21/14 Time: 23:32Sample: 2005M07 2014M10Lags:3Null Hypothesis:Obs F-StatisticProb.1082.777600.04511.342860.2648P does not Granger Cause DLE DLE does not Granger Cause P由上述结果可知，在5%的置信水平下，P是die的格兰杰原因，即全国房地产开发业综合景气指数是人民币对美元汇率变动幅度的格兰杰原因。5.2脉冲响应由于脉冲响应函数收到变量顺序的影响，因此其结果与分析的主观因素有关，对于 这三个变量：DLE R P,按照中国市场目前现状，认为DLE外生性最强，p其次最后为r。故选取顺序为DLE P、R。Response to Cfiolesky One S D. Innovations ?2 S.E2U图5.1脉冲响应图5.3方差分解表5.4方差分解结果Variance Decom position of DLE:PeriodS.E.DLEP10.003710100.00000.00000020.00371899.982500.01750030.00376998.893111.10688540.00392997.909522.09048150.00396696.365083.63491860.00401994.218215.78179370.00407892.060357.93964980.00412989.8151510.1848590.00418287.6054512.39455100.00423185.5997514.40025110.00427683.8063816.19362120.00431682.2474817.75252130.00435180.9365819.06342140.00438179.8538420.14616150.00440678.9772421.02276160.00442678.2831821.71682170.00444277.7439622.25604180.00445477.3334522.66655190.00446477.0279322.97207200.00447176.8058323.19417210.00447676.6485523.35145220.00447976.5405123.45949230.00448276.4688723.53113240.00448376.4233623.57664250.00448476.3960023.60400260.00448576.3807123.61929270.00448576.3730623.62694280.00448676.3698923.63011290.00448676.3690623.63094300.00448676.3691923.63081310.00448676.3694723.63053320.00448676.3694623.63054330.00448676.3690023.63100340.00448676.3680723.63193350.00448676.3667523.63325360.00448676.3651623.63484VarianceDecompositionof P:PeriodS.E.DLEP10.5449360.25733799.7426620.9837341.37891298.6210931.4187241.20744898.7925541.8251420.82489299.1751152.1948950.59927299.4007362.5220960.45388299.5461272.8070260.38586299.6141483.0507090.37289099.6271193.2558400.40512599.59488103.4259920.46978699.53021113.5649130.55340199.44660123.6765910.64929299.35071133.7649360.75050199.24950143.8336290.85127199.14873153.8860880.94810499.05190163.9253751.03814598.96186173.9541801.11948298.88052183.9748111.19116998.80883193.9892071.25283598.74717203.9989591.30464098.69536214.0053421.34717398.65283224.0093541.38127898.61872234.0117561.40797098.59203244.0131121.42833898.57166254.0138271.44346398.55654264.0141791.45436298.54564274.0143511.46195298.53805284.0144571.46702898.53297294.0145601.47025498.52975304.0146901.47216798.52783314.0148561.47318898.52681324.0150541.47363598.52636334.0152741.47373998.52626344.0155041.47366298.52634354.0157341.47350998.52649364.0159531.47334998.5266599.989.969.969.9卜9.9卜9.9699LQ9 8、9 8、9 008.9 008.9 008.9 008.9 008.9 008.9 008.9 00Q9008.9008.9008.9008.9008.9008.9 寸Q9 寸Q9 寸Q9008.9008.9008.928.9 008.9 寸Q998.9 寸6.920286Z0L6Z0L9 寸00ZOL6、L0L2OO0LZ.9.OO0LKoo-LL寸 OLCM、90.90 L oLnOL99.90 L68LO0L卜寸LnOL 999寸OL 99OO0L8、cm0looog80L0L 8OOOL L0O66 99.96 寸 6.96 9、寸6 寸、寸6 98.寸 6 99.96 9 寸.96 9 寸066 89.66 gl/LOL 8、L0L 9OOZ0L 80OO0L 寸OO.OOOL 卜0寸OI- CM、寸 OL000 丄 Low 20丄 Low 8丄 Low cmlolocm llolocm ololocm 6OOLO2906L02 gooLOCM 寸 oolocmLLI 6LI 002 寸2 卜寸2Lgl 9gl806L02 BLZ.OOLOCMCM9299l二 L co、 oooolocmaLL刃LLL8l cmlooocm寸 8l llooocm88l olooocml6iCM06L0CMloolocm99.90 L LL.90L 9 寸.90L69.90 L 寸、90L 66寸OL 8寸寸OL 寸OLOO9OO0L cmoooool 99Z0L &LOL 8、L0L 96Z0L 26OO0L 00- 寸LgCMOODOOCM 803002 cmtoocm LLgoCM otoocm 602002 802002 2.02002 902002 902002 寸 02002 0002002 CMogoCM 82002 cmlooocm llooocm olooocm 6990022008-032008-042008-052008-062008-072008-082008-092008-102008-112008-122009-012009-022009-032009-042009-052009-062009-072009-082009-09H 轴旺556 O0000 O0000 O00卜 O009 O0000CM O00CM O00CM O0000卜6 l96 l913E1aa旺H 轴旺1仃|4U|2005-112006-012011-04103.196.52013-0297.926.282011-05103.26.482013-0397.566.272011-06101.756.472013-0497.356.222011-07101.56.442013-0597.266.182011-08101.126.392013-0697.296.182011-09100.416.352013-0797.396.182011-10100.276.322013-0897.296.172011-1199.876.352013-0997.256.152011-1298.896.32013-1096.886.142012-0198.396.312013-1196.386.132012-0297.896.292013-1297.216.12012-0396.926.292014-0197.066.112012-0495.626.282014-0296.916.122012-0594.96.342014-0396.46.152012-0694.716.322014-0495.796.162012-0794.576.332014-0595.026.172012-0894.646.342014-0694.846.152012-0994.396.342014-0794.826.172012-1094.566.32014-0894.796.162012-1195.716.292014-0994.726.152012-1295.596.292014-1094.766.152013-0196.7556.28存在问题1 在进行单位根检验时，对于阶数的确定根据信息准则，那么在单位根检验之前是需要先 进行回归，确定 阶数后在进行单位根检验么？2、当数据不全时如何补全数据。3、初步选择滞后阶数时，是否可以参考单位根检验的滞后阶数。4、分析脉冲响应函数图时，位于主对角线之外的图是否应该满足同向影响的关系，即分析 A、B 两个变量 的脉冲响应函数，若A对B是负向影响，那B对A也应该是负向影响。