时间序列分析——VAR模型实验

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

2、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：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

3、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：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。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-1+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, maxl

4、ag=12)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-3.031673 0.0351Test critical values:1% level-3.4919285% level-2.88841110% level-2.581176*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(DLE)Method: Least SquaresDate: 11/15/

5、14 Time: 20:20Sample (adjusted): 2005M11 2014M10Included observations: 108 after adjustmentsVariableCoefficientStd. 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-0.0008880.000470-1.8875920.0

6、619R-squared0.450240    Mean dependent var1.15E-05Adjusted R-squared0.434382    S.D. dependent var0.005058S.E. of regression0.003804    Akaike info criterion-8.269046Sum squared resid0.001505    Schwarz criterion-8.16970

7、8Log likelihood450.5285    Hannan-Quinn criter.-8.228768F-statistic28.39119    Durbin-Watson stat2.061613Prob(F-statistic)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

8、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: 3 (Automatic - based on SIC, maxlag=12)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-3.972457 0.0124Test criti

9、cal 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%的置信水平下，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 Estimates

10、 Date: 11/22/14 Time: 22:20 Sample (adjusted): 2005M11 2014M10 Included observations: 108 after adjustments Standard errors in ( ) & t-statistics in DLEPDLE(-1) 0.063183-19.12274 (0.09626) (14.1374) 0.65638-1.35263DLE(-2) 0.116798 15.42129 (0.096

11、04) (14.1052) 1.21615 1.09330DLE(-3) 0.245260 16.39171 (0.09617) (14.1243) 2.55030 1.16053P(-1)-9.04E-05 1.490708 (0.00066) (0.09765)-0.13593 15.2656P(-2)-0.000583-0.355442 (0.00118) (0.17380)-0.49226-2.04508P(-3) 0.000346-0.160740 (0.00067

12、) (0.09872) 0.51479-1.62821C 0.031328 2.571540 (0.01274) (1.87084) 2.45943 1.37454 R-squared 0.295033 0.979509 Adj. R-squared 0.253154 0.978292 Sum sq. resids 0.001390 29.99247 S.E. equation 0.003710 0.544936 F

13、-statistic 7.044848 804.6767 Log likelihood 454.8094-84.06138 Akaike AIC-8.292766 1.686322 Schwarz SC-8.118924 1.860164 Mean dependent-0.002527 100.2406 S.D. dependent 0.004293 3.698585 Determinant resid covariance (dof adj.) 

14、;4.08E-06 Determinant resid covariance 3.57E-06 Log likelihood 370.8871 Akaike information criterion-6.609021 Schwarz 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 P Exogenous variables: C Date: 11/22/14 T

15、ime: 22:22Sample: 2005M07 2014M10Included observations: 99 LagLogLLRFPEAICSCHQ0 134.7784NA  0.000234-2.682392-2.629965-2.6611801 302.5627 325.3999 8.57e-06-5.991165-5.833886-5.9275302 329.0230 50.24783 5.45e-06-6.444909 -6.182775* -6.338849

16、*3 334.3733  9.943949*  5.30e-06* -6.472187*-6.105200-6.3237044 337.4531 5.599742 5.40e-06-6.453598-5.981758-6.2626915 339.7589 4.099176 5.60e-06-6.419372-5.842679-6.1860416 345.0498 9.192324 5.46e-06-6.445451-5.763905-6.1696

17、967 345.5484 0.846076 5.87e-06-6.374716-5.588316-6.0565378 346.7369 1.968760 6.23e-06-6.317917-5.426663-5.9573149 352.5801 9.443639 6.01e-06-6.355154-5.359047-5.95212810 353.7714 1.877082 6.39e-06-6.298411-5.197451-5.85296111 354.3649&

18、#160;0.911279 6.87e-06-6.229594-5.023780-5.74172012 356.4617 3.134644 7.18e-06-6.191146-4.880479-5.660848 * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike

19、information criterion SC: Schwarz information criterion 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3，此外取滞后阶数为2(SC为  -6.182775)或取滞后阶数为3(SC为-6.105200)时，两者SC值相差不是很大。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 Estimates Dat

20、e: 11/22/14 Time: 22:23 Sample (adjusted): 2005M11 2014M10 Included observations: 108 after adjustments Standard errors in ( ) & t-statistics in DLEPDLE(-1) 0.063183-19.12274 (0.09626) (14.1374) 0.65638-1.35263DLE(-2) 0.116798 15.42129 (0.09604) 

21、(14.1052) 1.21615 1.09330DLE(-3) 0.245260 16.39171 (0.09617) (14.1243) 2.55030 1.16053P(-1)-9.04E-05 1.490708 (0.00066) (0.09765)-0.13593 15.2656P(-2)-0.000583-0.355442 (0.00118) (0.17380)-0.49226-2.04508P(-3) 0.000346-0.160740 (0.00067) (0

22、.09872) 0.51479-1.62821C 0.031328 2.571540 (0.01274) (1.87084) 2.45943 1.37454 R-squared 0.295033 0.979509 Adj. R-squared 0.253154 0.978292 Sum sq. resids 0.001390 29.99247 S.E. equation 0.003710 0.544936 F-statisti

23、c 7.044848 804.6767 Log likelihood 454.8094-84.06138 Akaike AIC-8.292766 1.686322 Schwarz SC-8.118924 1.860164 Mean dependent-0.002527 100.2406 S.D. dependent 0.004293 3.698585 Determinant resid covariance (dof adj.) 4.08E-06

24、 Determinant resid covariance 3.57E-06 Log likelihood 370.8871 Akaike information criterion-6.609021 Schwarz 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：4.4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 P Exogen

25、ous variables: C Lag specification: 1 3Date: 11/22/14 Time: 22:27     RootModulus 0.883466 - 0.097039i 0.888779 0.883466 + 0.097039i 0.888779 0.670300 0.670300-0.321875 - 0.501863i 0.596213-0.321875 + 0.501863i 0.596213-0.239592&#

26、160;0.239592 No root lies outside the unit circle. VAR satisfies the stability condition.图4.6 VAR模型平稳性检验的图形显示由上表和上图可知，VAR模型的特征方程的根均在单位园内，因此VAR模型是平稳的。下面进行残差的自相关性的检验，检验结果如下：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

27、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: 3 Null Hypothesis:ObsF-StatisticProb.  P does not Granger Cause DLE 108 2.777600.0451 DLE does not Granger Cause P 1.

28、342860.2648由上述结果可知，在5%的置信水平下，P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。图5.1 脉冲响应图5.3方差分解 表5.4 方差分解结果 Variance Decomposition of DLE: PeriodS.E.DLEP 1 0.003710 100.0000

29、60;0.000000 2 0.003718 99.98250 0.017500 3 0.003769 98.89311 1.106885 4 0.003929 97.90952 2.090481 5 0.003966 96.36508 3.634918 6 0.004019 94.21821 5.781793 7 0.004078 92.06035 7.9

30、39649 8 0.004129 89.81515 10.18485 9 0.004182 87.60545 12.39455 10 0.004231 85.59975 14.40025 11 0.004276 83.80638 16.19362 12 0.004316 82.24748 17.75252 13 0.004351 80.93658 19.06

31、342 14 0.004381 79.85384 20.14616 15 0.004406 78.97724 21.02276 16 0.004426 78.28318 21.71682 17 0.004442 77.74396 22.25604 18 0.004454 77.33345 22.66655 19 0.004464 77.02793 22.97

32、207 20 0.004471 76.80583 23.19417 21 0.004476 76.64855 23.35145 22 0.004479 76.54051 23.45949 23 0.004482 76.46887 23.53113 24 0.004483 76.42336 23.57664 25 0.004484 76.39600 23.60

33、400 26 0.004485 76.38071 23.61929 27 0.004485 76.37306 23.62694 28 0.004486 76.36989 23.63011 29 0.004486 76.36906 23.63094 30 0.004486 76.36919 23.63081 31 0.004486 76.36947 23.63

34、053 32 0.004486 76.36946 23.63054 33 0.004486 76.36900 23.63100 34 0.004486 76.36807 23.63193 35 0.004486 76.36675 23.63325 36 0.004486 76.36516 23.63484 Variance Decomposition of P: PeriodS

35、.E.DLEP 1 0.544936 0.257337 99.74266 2 0.983734 1.378912 98.62109 3 1.418724 1.207448 98.79255 4 1.825142 0.824892 99.17511 5 2.194895 0.599272 99.40073 6 2.522096 0.453882 99.5461

36、2 7 2.807026 0.385862 99.61414 8 3.050709 0.372890 99.62711 9 3.255840 0.405125 99.59488 10 3.425992 0.469786 99.53021 11 3.564913 0.553401 99.44660 12 3.676591 0.649292 99.35071&#

37、160;13 3.764936 0.750501 99.24950 14 3.833629 0.851271 99.14873 15 3.886088 0.948104 99.05190 16 3.925375 1.038145 98.96186 17 3.954180 1.119482 98.88052 18 3.974811 1.191169 98.80883&#

38、160;19 3.989207 1.252835 98.74717 20 3.998959 1.304640 98.69536 21 4.005342 1.347173 98.65283 22 4.009354 1.381278 98.61872 23 4.011756 1.407970 98.59203 24 4.013112 1.428338 98.57166&#

39、160;25 4.013827 1.443463 98.55654 26 4.014179 1.454362 98.54564 27 4.014351 1.461952 98.53805 28 4.014457 1.467028 98.53297 29 4.014560 1.470254 98.52975 30 4.014690 1.472167 98.52783&#

40、160;31 4.014856 1.473188 98.52681 32 4.015054 1.473635 98.52636 33 4.015274 1.473739 98.52626 34 4.015504 1.473662 98.52634 35 4.015734 1.473509 98.52649 36 4.015953 1.473349 98.52665附录

41、具体数据指标国房景气指数_当月人民币对美元期末汇率地区全国全国频度月月单位-人民币/美元2005-07101.978.112005-08101.768.12005-09101.428.092005-10101.028.082005-11100.698.082005-12100.618.072006-01100.768.062006-02101.058.042006-03101.468.022006-04101.618.022006-05101.878.022006-06102.9382006-07103.517.972006-08103.317.962006-09103.147.912006-

42、10103.47.882006-11103.927.842006-12102.967.812007-01102.427.782007-02101.787.742007-03101.227.732007-04102.657.712007-05103.327.652007-06103.637.622007-071047.572007-08104.487.562007-09104.997.512007-10105.747.472007-11106.597.42007-12106.457.32008-01106.117.192008-02105.557.112008-03104.727.022008-04104.0772008-05103.346.942008-06103.086.862008-07102.366.8420