时间序列分析——VAR模型试验

1、基于VAR模型的我国房地产市场与汇率波动的因果关系VAF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VAF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，不单彳对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，

2、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 P!4T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:E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

3、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lm,其时序图如下:LE图4.2 lm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lm进行一阶差分处理，去除趋 势性，得到新变量dlm,观察dlm的曲线图。CLE图4.3 DLE 的曲线图从图中可以看出，dle序列的趋势性基本已经消除，且新变量dle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 - bas

4、ed on SIC, maxlag=12)t-StatisticProb.MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(DLE)Method: Least SquaresDate: 11/15/14 Time: 20:20Sample (adjusted): 2005M11 2014M10Included observations: 108 after adjustmentsAugmented Dickey-Fuller test statistic-

5、3.0316730.0351Test critical values:1% level-3.4919285% level-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-squared0.450

6、240Mean dependent var1.15E-05Adjusted R-squared0.434382S.D. dependent var0.005058S.E. of regression0.003804Akaike info criterion-8.269046Sum squared resid0.001505Schwarz criterion-8.169708Log likelihood450.5285Hannan-Quinn criter.-8.228768F-statistic28.39119Durbin-Watson stat2.061613Prob(F-statistic

7、)0.000000单位根统计量 ADF=3.031673小于临界值，且P为0.0351 ,因此该序列不是单位根过程, 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：图4.5 P 的曲线图(补全)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 改序列是否平稳。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

8、: 3 (Automatic - based on SIC, maxlag=12)t-StatisticProb.*Augmented 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

9、此样本数量减少，在下面的操作中，所有的样本序列调整为2005-08至2014-10。4.2 模型参数识别3:先进行VAR模型的拟合，初步选定滞后阶数为表4.3 拟合输出结果Vector Autoregression EstimatesDate: 11/22/14 Time: 22:20Sample (adjusted): 2005M11 2014M10Included observations: 108 after adjustmentsStandard errors in ( ) & t-statistics in DLEPDLE(-1)0.063183-19.12274(0.096

10、26)(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)0.51479-1.6

11、2821C0.0313282.571540(0.01274)(1.87084)2.459431.37454R-squared0.2950330.979509Adj. R-squared0.2531540.978292Sum sq. resids0.00139029.99247S.E. equation0.0037100.544936F-statistic7.044848804.6767Log likelihood454.8094-84.06138Akaike AIC-8.2927661.686322Schwarz SC-8.1189241.860164Mean dependent-0.0025

12、27100.2406S.D. dependent0.0042933.698585Determinant resid covariance (dof adj.)4.08E-06Determinant resid covariance3.57E-06Log likelihood370.8871Akaike information criterion-6.609021Schwarz criterion-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 CriteriaEndogenous variables: DLE PExogenous

13、 variables: CDate: 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 indicates lag order selected by the criterionLR: seq

14、uential modified LR test statistic (each test at 5% level)FPE: Final prediction errorAIC: Akaike information criterionSC: Schwarz information criterion-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-06-6.4193

15、72-5.842679-6.1860416345.04989.1923245.46e-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

16、.87e-06-6.229594-5.023780-5.74172012356.46173.1346447.18e-06-6.191146-4.880479-5.6608483,此外取滞SC值相差不是HQ: Hannan-Quinn information criterion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， 很大。3.3模型参数估计选取了最优?t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 Estimate

17、sDate: 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)(1

18、4.1243)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)1.37454R-squared0.2950330.979509Adj. R-squared0.2531540.978292Sum sq.

19、resids0.00139029.99247S.E. equation0.0037100.544936F-statistic7.044848804.6767Log likelihood454.8094-84.06138Akaike AIC-8.2927661.686322Schwarz SC-8.1189241.860164Mean dependent-0.002527100.2406S.D. dependent0.0042933.698585Determinant resid covariance (dof adj.)4.08E-06Determinant resid covariance3

20、.57E-06Log likelihood370.8871Akaike information criterion-6.609021Schwarz criterion-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) + 0.0313

21、284849005P = - 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 PolynomialEndogenous variables: DLE PExogenous variables: C

22、Lag specification: 1 3Date: 11/22/14 Time: 22:27RootModulus0.883466 - 0.097039i0.8887790.8887790.883466 + 0.097039i0.6703000.596213-0.321875 + 0.501863i0.596213-0.2395920.239592No root lies outside the unit circle.VAR satisfies the stability condition.Inverse Roots of AR Characteristic Polynomialo.o

23、-0.5-150 5-1.0050.00.5-10-0.670300 -0.321875 - 0.501863i图4.6 VAR模型平稳性检验的图形显示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，因此卜面进行残差的自相关性的检验，检验结果如下:AiitncorrelatiQns with 2 Ski Frr RoundsCortPDLE(.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

24、。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5.1 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.P does not Granger Cause DLEDLE does not Granger Cause P1082.777601.342860.04510.2648由上述结果可知，在5%勺置信水平下，P

25、是dle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 Ctiolesky One S D. Innovations ?2 S.EKe&panse ol IH to r-1.0图5.1脉冲响应图5.3 方差分解表5.4方差分解结果VarianceDecompo sitionof DLE:PeriodS.E.DLEP10

26、.003710100.00000.00000020.00371899.982500.01750030.00376998.893111.10688540.00392997.909522.09048150.00396696.365083.63491860.00401994.218215.78179370.00407892.060357.93964980.00412989.8151510.1848590.00418287.6054512.39455100.00423185.5997514.40025110.00427683.8063816.19362120.00431682.2474817.7525

27、2130.00435180.9365819.06342140.00438179.8538420.14616150.00440678.9772421.02276160.00442678.2831821.71682170.00444277.7439622.25604180.00445477.3334522.66655190.00446477.0279322.97207200.00447176.8058323.19417210.00447676.6485523.35145220.00447976.5405123.45949230.00448276.4688723.53113240.00448376.

28、4233623.57664250.00448476.3960023.60400260.00448576.3807123.61929270.00448576.3730623.62694280.00448676.3698923.63011290.00448676.3690623.63094300.00448676.3691923.63081310.00448676.3694723.63053320.00448676.3694623.63054330.00448676.3690023.63100340.00448676.3680723.63193350.00448676.3667523.633253

29、60.00448676.3651623.63484VarianceDecompo sitionof P:PeriodS.E.DLEP10.5449360.25733799.7426620.9837341.37891298.6210931.4187241.20744898.7925541.8251420.82489299.1751152.1948950.59927299.4007362.5220960.45388299.5461272.8070260.38586299.6141483.0507090.37289099.6271193.2558400.40512599.59488103.42599

30、20.46978699.53021113.5649130.55340199.44660123.6765910.64929299.35071133.7649360.75050199.24950143.8336290.85127199.14873153.8860880.94810499.05190163.9253751.03814598.96186173.9541801.11948298.88052183.9748111.19116998.80883193.9892071.25283598.74717203.9989591.30464098.69536214.0053421.34717398.65

31、283224.0093541.38127898.61872234.0117561.40797098.59203244.0131121.42833898.57166254.0138271.44346398.55654264.0141791.45436298.54564274.0143511.46195298.53805284.0144571.46702898.53297294.0145601.47025498.52975304.0146901.47216798.52783314.0148561.47318898.52681324.0150541.47363598.52636334.0152741

32、.47373998.52626344.0155041.47366298.52634354.0157341.47350998.52649364.0159531.47334998.52665附录具体数据国房景气指数当人民币对美元期末2008-05103.346.94指标月汇率2008-06103.086.86地区全国全国2008-07102.366.84频度月月2008-08101.786.83单位-人民币/美元2008-09101.156.822005-07101.978.112008-1099.686.832005-08101.768.12008-1198.466.832005-09101.4

33、28.092008-1296.466.832005-10101.028.082009-0195.666.842005-11100.698.082009-0294.866.842005-12100.618.072009-0394.746.842006-01100.768.062009-0494.766.832006-02101.058.042009-0595.946.832006-03101.468.022009-0696.556.832006-04101.618.022009-0798.016.832006-05101.878.022009-08100.086.832006-06102.938

34、2009-09101.086.832006-07103.517.972009-10102.036.832006-08103.317.962009-11102.786.832006-09103.147.912009-12103.666.832006-10103.47.882010-01104.5656.832006-11103.927.842010-02105.476.832006-12102.967.812010-03105.896.832007-01102.427.782010-04105.666.832007-02101.787.742010-05105.076.832007-03101.227.732010-06105.066.782007-04102.657.712010-07104.726.782007-05103.327.652010-08104.116.812007-06103.637.622010-09103.