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1、Four short words sum up what has lifted most successful individuals above the crowd: a little bit more.-author-dateVAR案例分析VAR案例分析 VAR模型的应用举例1 案例分析的目的 股市对居民储蓄存款存在分流的作用。一般来说，若股市出现牛市，资金会从存款性金融机构流向股市，居民储蓄存款下降或者增速会减缓。从当前我国经济发展趋势来看，居民储蓄存款与股市交易额均呈上升趋势。那么两者是否存在相互影响呢？本案例将分析居民储蓄与股市之间的这种联动效应。2 实验数据本实验选取从1996年到
2、2008年4月的月度数据。整理如下。表1 股市交易额与居民存款余额 单位：亿元日期沪深股市交易总额居民储蓄存款余额日期沪深股市交易总额居民储蓄存款余额1996.1143.493230356.542002.43114.39279728.21996.263.9416432026.252002.51924.59480394.31996.3217.75633296.482002.64303.07681711.791996.4873.422134018.532002.73227.30582527.91996.51163.7434622.12002.81946.36683275.971996.61812.
3、86235457.912002.91460.39184139.051996.72718.6236048.672002.101181.98984725.131996.81685.59136705.82002.111908.61785693.491996.91862.16437085.172002.121781.22886910.651996.104012.437671.422003.13060.93390677.631996.113818.9737917.262003.21666.80292824.211996.124238.9238520.82003.32120.63794567.841997
4、.11829.17939038.182003.45848.29795194.121997.21493.92540869.122003.53209.4596351.671997.34263.841580.972003.62557.1597674.571997.45127.9242112.162003.72351.91798590.91997.54640.9642295.162003.81519.42799255.581997.63080.9542771.162003.91661.203100888.61997.72415.7343312.52003.101615.799101381.91997.
5、81858.37843914.922003.112824.502102235.41997.91625.71344139.452003.124359.423103617.71997.102081.67344720.332004.13649.76109232.71997.111586.9545068.432004.27215.755110646.41997.121570.19546279.82004.35792.181111872.21998.11716.977464832004.45270.107112175.41998.21171.90648537.542004.51823.421112610
6、.21998.31703.31248686.482004.62627.057113792.51998.43624.4448984.62004.72548.009114253.21998.53322.3497002004.81880.649114489.61998.62593.349949.892004.93978.274115458.71998.71761.80550749.822004.102893.0651160011998.81497.88250900.912004.113045.002117617.91998.92149.00851580.742004.122094.784119555
7、.41998.101861.7952247.772005.11754.347122237.31998.112194.2452952.322005.22021.07127823.41998.121040.05853407.52005.33047.432129259.41999.11138.81954293.672005.43036.061129816.81999.2334.019656767.452005.51497.376130577.41999.31757.27757814.652005.63177.354132339.11999.42063.44558369.072005.72243.73
8、133656.41999.52719.5958967.842005.84776.3331345051999.69562.5959173.482005.94132.053136316.31999.75538.0259147.552005.102097.632136827.11999.83665.4759187.262005.112301.058138504.31999.92705.1259364.312005.122350.0861410511999.101250.08759269.92006.13635.936148008.41999.111558.04959185.382006.23726.
9、141151179.61999.121482.01359621.82006.34074.6251528192000.14443.45860241.82006.47308.7261534012000.26621.81962270.32006.510926.12153523.42000.38877.35562492.292006.69159.456154996.92000.45960.92662536.122006.78197.536155131.92000.54298.7162195.392006.85526.955156282.12000.66251.17762842.382006.96705
10、.497158108.92000.75436.68662841.52006.106793.858158033.42000.86650.38762861.112006.1110586.65159716.72000.93167.35963243.272006.1215861.8161587.32000.102706.93163122.342007.126191.65161968.62000.115235.81863492.062007.217845.01171042.62000.123985.7964332.382007.332526.3172607.72001.13161.01666547.31
11、2007.449865.94170932.72001.22055.59167343.362007.559864.231680402001.35368.46568365.132007.655444.85169651.62001.45845.64668618.462007.733764.63169567.22001.54752.868393.542007.855638.96169171.52001.65190.08669628.582007.947008.27169038.12001.73344.07469677.772007.1035870.9163957.62001.82677.7117055
12、8.482007.1125750.72166561.12001.102147.89271818.812007.1229632.95172616.12001.122193.07173762.432008.147340.36174347.92002.12072.05674953.712008.221457.51183960.22002.21341.43378114.332008.329058.96187414.92002.34917.91578728.32008.427832.14188389.14.3 VAR模型的构建4.3.1 数据平稳性检验考虑到本例中的数据是宏观经济月度数据，先消除季节性特
13、征后再进行分析。另外数据变动趋势过大，本例还对数据进行了对数平滑处理。下图是两个变量经过季节性调整并取对数后的新序列，其中lsa表示居民储蓄额，ltr表示股市交易总额。在主窗口命令行中输入：genr lsa=log(savingsa)genr ltr=log(tradingsa)图1 居民储蓄额与股市交易额对数值的对比图根据图形特征选取同时存在截距项和趋势项进行单位根检验。分别在lsa和ltr窗口中点击view/unit root test/。Lsa单位根检验的结果：Null Hypothesis: LSA has a unit rootExogenous: Constant, Linear
14、TrendLag Length: 0 (Automatic based on SIC, MAXLAG=13)t-StatisticProb.*Augmented Dickey-Fuller test statistic-3.2957650.0711Test critical values:1% level-4.0225865% level-3.44111110% level-3.145082*MacKinnon (1996) one-sided p-values.Ltr单位根检验的结果：Null Hypothesis: LTR has a unit rootExogenous: Constan
15、t, Linear TrendLag Length: 0 (Automatic based on SIC, MAXLAG=13)t-StatisticProb.*Augmented Dickey-Fuller test statistic-4.1025970.0078Test critical values:1% level-4.0225865% level-3.44111110% level-3.145082*MacKinnon (1996) one-sided p-values.从而lsa和ltr在10的显著性水平上均是平稳序列。3.2 VAR模型滞后阶数的选择选取view/lag str
16、ucture/lag length criteria。由于总共有146个月度样本，选取最大的可能滞后阶数为12。不同判断标准下滞后阶数的选取：VAR Lag Order Selection CriteriaEndogenous variables: LSA LTRExogenous variables: CSample: 1 146Included observations: 134LagLogLLRFPEAICSCHQ0-241.1002NA0.1290713.6283613.6716123.6459361325.25601107.3532.92e-05*-4.765015*-4.63526
17、1*-4.712287*2327.87885.0499852.98e-05-4.744460-4.528203-4.6565803329.27502.6463843.10e-05-4.705596-4.402837-4.5825654332.53006.0728303.14e-05-4.694478-4.305215-4.5362945336.75877.7630833.13e-05-4.697891-4.222126-4.5045556337.41641.1879343.29e-05-4.648007-4.085739-4.4195197341.99248.1273933.26e-05-4.
18、656603-4.007832-4.3929638342.91091.6039273.42e-05-4.610610-3.875337-4.3118199349.213710.81825*3.31e-05-4.644980-3.823205-4.31103710349.85901.0883893.48e-05-4.594910-3.686632-4.22581611353.24775.6141723.52e-05-4.585787-3.591006-4.18154012355.33513.3959453.63e-05-4.557241-3.475958-4.117842从以上分析结果可以看出，
19、FPE、AIC、SC和HQ都得出滞后阶数为1时VAR模型时最优的。因此选取的最优滞后阶数为1，即k=1。3.3 VAR模型的估计下表是滞后阶数为1时VAR模型的估计结果。VAR(1)的估计结果：Sample (adjusted): 2 146Included observations: 145 after adjustmentsStandard errors in ( ) & t-statistics in LSALTRLSA(-1)1.0011700.228703(0.00255)(0.09860) 393.219 2.31943LTR(-1)-0.0040830.808610(0.0011
20、9)(0.04622)-3.42147 17.4964C0.032687-0.987968(0.02389)(0.92510) 1.36837-1.06795R-squared0.9994400.808826Adj. R-squared0.9994320.806134Sum sq. resids0.02034630.51501S.E. equation0.0119700.463567F-statistic126697.4300.3900Log likelihood437.4447-92.75374Akaike AIC-5.9923411.320741Schwarz SC-5.9307541.3
21、82329Mean dependent11.311298.194037S.D. dependent0.5022691.052838Determinant resid covariance (dof adj.)3.01E-05Determinant resid covariance2.89E-05Log likelihood346.2668Akaike information criterion-4.693335Schwarz criterion-4.570159从表中可以看出VAR模型的参数估计大多显著。3.4 VAR模型的检验VAR模型的检验包括VAR模型的平稳性检验，以及残差的独立性检验。
22、选择view/lag structure/AR roots table 或者AR roots graph可以得到平稳性检验的结果。Roots of Characteristic PolynomialEndogenous variables: LSA LTRExogenous variables: CLag specification: 1 1RootModulus0.9961920.9961920.8135880.813588No root lies outside the unit circle.VAR satisfies the stability condition.因此VAR模型满足平
23、稳性的条件。选择view/residual tests/correlograms，得到各方程残差项的自相关图。所以残差不存在自相关性，满足独立性假设。3.5 VAR模型的预测前文介绍，与ARMA模型不同，在VAR估计结果的窗口中没有直接预测的选项，此时需要建立model进行预测。命令：make model Assign all f上述命令表示建立模型进行预测，预测序列名称后缀名为f。下图是动态预测结果。4 VAR模型的应用4.1 格兰杰因果检验将lsa与ltr建立group，点击view/granger causality。根据VAR模型的滞后阶数来决定滞后阶数，本例中选择滞后阶数为1。Pai
24、rwise Granger Causality TestsSample: 1 146Lags: 1Null Hypothesis:ObsF-StatisticProb.LTR does not Granger Cause LSA14511.70640.0008LSA does not Granger Cause LTR5.379780.0218从中可以看出，ltr与lsa之间互为格兰杰原因。这说明居民储蓄与股票交易变动之间相互影响。4.2 脉冲响应脉冲响应函数受到变量顺序的影响，因此其结果与分析的的主观因素有关。在VAR模型输出窗口中，选择view/impulse response观察第二个图
25、形，股市交易量对居民储蓄是负向影响关系，这验证了股市的分流效应。从时间长短来看，股市交易对居民储蓄的长期影响要大于短期影响，而居民储蓄对股市交易的短期影响要显著些。4.3 方差分解在VAR输出窗口中，选择view/variance decompositionVariance Decomposition of LSA:PeriodS.E.LSALTR10.011970100.00000.00000020.01723898.820201.17979530.02155596.774103.22590240.02542294.385675.61433450.02900991.953918.046090
26、60.03238689.6337010.3663070.03559187.4952512.5047580.03864485.5619414.4380690.04155983.8326616.16734100.04434882.2944917.70551110.04702080.9296319.07037120.04958179.7190920.28091130.05204078.6444721.35553140.05440477.6889122.31109150.05667776.8372923.16271160.05886776.0763323.92367170.06097975.39447
27、24.60553180.06301874.7816925.21831190.06498774.2293425.77066200.06689373.7299726.27003210.06873873.2771526.72285220.07052672.8653227.13468230.07226172.4897027.51030240.07394672.1461427.85386250.07558371.8310528.16895260.07717571.5413028.45870270.07872571.2741828.72582280.08023571.0273128.97269290.08
28、170770.7986229.20138300.08314270.5862829.41372310.08454470.3887029.61130320.08591270.2044629.79554330.08725070.0323229.96768340.08855769.8711730.12883350.08983669.7200330.27997360.09108869.5780430.42196Variance Decomposition of LTR:PeriodS.E.LSALTR10.4635672.15000897.8499920.5959112.06915297.9308530
29、.6680601.99464098.0053640.7109031.92815198.0718550.7372061.87088898.1291160.7535841.82354198.1764670.7638261.78630998.2136980.7702201.75897198.2410390.7741901.74097798.25902100.7766351.73155798.26844110.7781251.72981398.27019120.7790251.73480098.26520130.7795681.74558698.25441140.7799011.76128998.23
30、871150.7801141.78110998.21889160.7802661.80433198.19567170.7803901.83033398.16967180.7805061.85858198.14142190.7806251.88862498.11138200.7807541.92008098.07992210.7808941.95263698.04736220.7810451.98602898.01397230.7812082.02004397.97996240.7813812.05450597.94550250.7815622.08927097.91073260.7817512
31、.12422297.87578270.7819452.15926797.84073280.7821442.19432797.80567290.7823462.22934497.77066300.7825522.26426697.73573310.7827592.29905597.70095320.7829672.33367997.66632330.7831762.36811397.63189340.7833862.40233997.59766350.7835952.43634197.56366360.7838042.47010697.52989Cholesky Ordering: LSA LTR从方差分解的结果来看，居民储蓄波动的部分原因源自于股市交易量的变动，而股市交易量的变动更多是源于自身的影响。这与脉冲响应的结果一致。-