计量经济学实验报告(实验项目：时间序列计量经济学模型)(2)

1、实验项目：时间序列计量经济学模型一实验目的通过上机实验掌握计量经济学软件EViews，运用EViews软件进行时间序列计量经济学模型的分析，掌握时间序列计量经济学模型，包括建立模型，了解其单整性、平稳性。二预备知识单位根检验、单整性检验、ADF检验、最小二乘估计原理。三实验内容F表给出了 1978 2006年中国居民消费价格指数CPI.(1990年=100)年份CPI年份CPI年份CPI197846.21198882.31998202.59197947.071989971999199.72198050.6219901002000200.55198151.91991103.422001201.9

2、4198252.951992110.032002200.321983541993126.22003202.73198455.471994156.652004210.63198560.651995183.412005214.42198664.571996198.662006217.65198769.31997204.21做出时间序列CPI的样本相关图，并通过图形判断该序列时间序列的平稳性。对CPI序列进行单位根检验，以进一步明确它们的平稳性。检验CPI的单整性。四实验步骤(一)启动软件包Eviews 的启动步骤：双击Eviews快捷方式，进入EViews窗口；或点击开始/程序/ Eviews 6

3、，进入EViews窗口。（二）创建工作文件。1建立工作文件并录入数据，如图1所示。口 Series： CP! Workfile: UN TITLE D:UntFtled京 |图12平稳性检验2.1平稳性的图示判断给出一个随机时间序列，首先可以通过该序列的事件路径图来粗略地判断它是否是平稳的。使用语句 T=TREND+197产生时间点的序列 T，画出CPI跟时间T的关系图，即时序 图，如图2所示。 Series; CPI Workfile: UNTTTLED；!Urrtitfed 口【回爭W&fljppt|Object| Properties Print Name F亡皀z皀 | Sam

4、ple| Genr| She皀t| Gnph| Stats| IcJent|CPI由图2,我们可以直观地看到CPI关于时间T有明显递增的趋势，不同时间段的均值不同，有持续上升，即CPI序列不平稳。当然，这种直观的图示也常长生误导，因此需要进行进一步的判断。2.2样本自相关图判断点击主界面 Quick'Series Statistics'Correlogram.，在弹出的对话框中输入CPI，点击0K就会弹出Correlogram Specification对话框，选择 Level，并输入要输出的阶数（一般为12），点击OK即可得到CPI的样本相关函数图，如图3所示。Correlo

5、gram SpecrficationCorrelogram ofLevel1st differenceOK |2nd differenceLags to indude1 cancelDate: OS/13/12 Time: 14:113Sample: 197B 2006Included obser-ations: 29AC PAG Q-Stat Prot>Autocorrelation Partial Correlation11匚1< LII| II| 1I匚1| rII匚II匚1匚II| II1110.9310 93127.8430.00020 847-0.153517200,0

6、0030755-0.08971 440O.QOQ40.662-0.05487 2050.00050.566-0.08099.1870.00060.462-0.113107 530.00070.352-0.108112600.00080.239-0.099115050.00090.120-0 137115.700.00010-0 004-0 139115.70O.QOQ11-0.120-0.063116420.00012-0.221-0.003119010.000图3一个时间序列的样本自相关函数定义为：n上、(Xt -X)(Xt .k -X)k =1,2,3,.t m2' (Xt -X)

7、t m易知，随着k的增加，样本自相关函数下降且趋于零。但从下降速度来看，平稳序列要比非平稳序列快得多。从上述样本相关函数图，可以看到CPI的样本相关函数是缓慢的递减趋 于零的，并没有像偏自相关函数那样的迅速减为零。所以，通过CPI的样本相关图，可初步判定该CPI时间序列非平稳。当然这中判断方法也是有一定的主观性的，下面我们进行客观性的判断，进一步明确CPI序列的平稳性。2.3单位跟检验（ADF检验）采用ADF检验对 CPI序列进行平稳性的单位根检验。点击主界面Quick'SeriesStatistics' Unit Root Test.，在弹出的 Series 对话框中输入 C

8、PI，点击 OK 就会出现Un it Root Test对话框，如图 4所示。Unit Root TestTest typeAugmented Dicke y-FdlerL 的 length Automate se ection:|sdi脚ar? Inft Criterion |Maxim jm lags: pUser speafied :11Test for unit root inLevel广 1st diffierence厂 2nd differenceIndud亡 in test equatian Intercept' Trend and interceptf' Non

9、 亡OK I CancelUnit Root Test对话框的设置。其中Test for unit root in栏中，Level是水平序列，1st是一阶差分序列，2nd是二阶差分序列；In elude in test equation 栏中，In tercept 是常数项，对应 ADF检验中的第二个模型，Trend and in tercept是趋势项加常数项，对应ADF检验中的第三个模型，None是没有趋势项跟常数项，对应ADF检验中的第一个模型；右侧的Lag length是滞后阶数的确定，系统默认是用SC值确定，且默认最大滞后阶数为6阶。本题中，对于 CPI序列的单位根检验是选择Leve

10、l项，ADF检验结果如下。对于模型3:VariableCoeFicientStd. Errort-StatisticProb.CPK-1)-0.2392740.Q92967-2.5737460.0212D(CPI( 1)1 2B37390.2010396.4104040.0000D(CPI(-2)-0.7802050.341234-2.2864210.0372D(CPI(-3)0.7735290.3792252.0529490,0579D(CPl(-4)-0.5530160.339560*1.6206280.1242D(CPl(-5)0.5222950.2220242 3524300.0327

11、C07251753 2420450.2236700.8260TREND(1978)1.3849660.80236B2.3492540 0329R-squared0.817179Mean dependent var7.115217Adjusted R-squared0.731863S.D. dependentvar8.605129S.E. of regression4.455904kaike info criterion6.094545Sum squared resid297.8252Schwarz criterion6.439500Log likelihood-52.08727Hannan-Q

12、uinn criter.6193975F-statistic9.578226Durbin-Watson stat1.920843ProbfF-statisti c)0.000146讷皀矗 | Pck | Object Prop亡巾凸 | Pint|NBm|FEZE Sample Gen” She已t| Gnph Stats IdentAugmented Dickey-Fuller Unrt Root Test on CPIO Series; CPI Warkfile; UNTTTLED：!Untitled-a- 回'iewj Proc | Object | Properties Pri

13、nt (Name (Freeze Sample Genr| Sheet | Graph StatsIdent |Augmented Dickey-Fuller Unrt Root Test on CPINull Hypothesis: CPI has a unit rootExogenous: Constant. LinearTrendLag Length: 5 (Automatic based on SIC, MAXLAG=6)t-StaVsticProb*Augmented Dickey*Fuller test statistic-2.5737460.2939Test critical v

14、alues:1% level 5% level 10% level-4.416345-3.622033-3.248592'MacKinnon(1996) one-sided pvalues.Augmented Dickey-Fuller Test Equation Dependent Variable' D(CPI)Method: Least SquaresDate: 06/13/12 Time: 14:20Sample (adjusted): 1984 2006Included obseations: 23 after adjustments Series: CPT Work

15、file: UNTTTLEDtiUrrtitled图5可以看到伪概率 P =0.2939 ，在5%的水平下是接受有单位根的原假设的。模型3的估计结果为：t -3CPI t =0.7251.885 t -0.239 CPI1.289 CPI t 4 一 0.780 CPI 0.779 CPI 0.553 ：CPI j 0.522 CPI 心其中，趋势项参数:的估计值的t统计量为t = 2.349254 ，查ADF分布临界值表得，模 型3样本个数为25个（最接近的个数）时£加.025 = 3.25，即接受0 =0的原假设，于是可与 进行模型2的估计。对于模型2:口 Senes:匚円 Wo

16、rkfile： UNTTTLED:UntitledVi皀矗 | Objxt| Prop皀rtiEE |Sample GenrJSheEt G召ph|5tats Iident|Augmented Dickey-Fuller Unit Root Test on CPINull Hypothesis: CPI has a unit rootExogenous: ConstantLag Length: 2 (Automatic based on SIC, L1AXLAG=6)t-StatisticProb*Augmented Dickey*Fuiier test statistic-0.4725590

17、.S815Test critical values:1% level5% level10% level071145 了 -2.981038 -2.6299Q6* MacKinnon(1996) one-sided p<alues.Augmented Dickey-Fuller Test Equation Dependent Variable D(CPI Method: Least SquaresDate: 06/13/12 Ums: 14:115Sample (adjusted): 19B1 2006Included observations: 26 after adjustmentsr

18、 Series; CPT Warkfile: UNTTTLEDjiUrrtitled讷世理 | Pot | Objgut | Prop皀rtiEW | Pint|N日m皀 | F亡皀z皀 | Sample | Genr | She皀t| Gnph | Stats 11日皀nt |Augmented Dickey-Fuller Unit Root Test on CPI 匕UHWM,岳口! 7乂2 0>1 口Date: 05/13/12 Time: 14:15Sample (adjusted): 1961 2006Included observations: 26 alter adjust

19、mentsVariableCoefficientStd. Errort-StatisticProb.CPI(-1)-0.0075100.015893*0.4725590,6412D(CPI(-1)1.12759701787566.3080170.0000D(CPI-2)-0.524934Q181473-2 8926340.0084C34837332.3570231.4776680.1537R-squared0.581683Mean dependent var6.424231Adjusted R-sqjared0.633276S.D dependentvar8304869S.E. of regr

20、ession4.994839Akaike info criterion6 195326Sum squared resid54B.a651Schwarz criterion6.386879Log likelihood-76.53923Hannan-Quinn criter.6.2510&2F-statistic1570448Durbin-Watson stat1 746395ProbfF-statisti c)0.000011可以看到伪概率 P =0.8815，在5%的水平下是接受有单位根的原假设的。模型2的估计结果为：.：CPI t = 3.484 0.0075 CPI t1.128

21、. ：CPI t一 0.525 . ：CPI tj其中，常数项参数:-的估计值的t统计量为t =1.477668 ，查ADF分布临界值表得，模 型2样本个数为25个（最接近的个数）时o.o25 = 2.97，即接受a =0的原假设，于是可与 进行模型1的估计。对于模型1 : Series: CPT Workfie： UNTITLED;:Untitd丫的| Proc Objxt| Prop皀rtis | Pint|Nmm|FZE | Sample | Genr | She皀t| Gmph | Stats | IcJent|Null Hypothesis: CPI has a unit rootE

22、xogenous: NoneLag Length: 2 Automatic based on SIC, MAXLAG=6)t-StatisticProb*Augmented Dickey*Fuller test statistic1.3821490.9541Test critical values:1% level &% level 10% level-2.656915-1 954414-1.609329'MacKinnon(1996) one-sided pvalues.Augmented Dickey-Fuller Test Equation Dependent Varia

23、ble D(CPI)Method: Least SquaresDate: 06/13/12 Time: 14:21Sample (adjusted): 1981 2006Included obseations: 26 after adjustments Series: CPI Workfile: UNTTTLED:iUrrtitled| 口 回卫讷皀呻 | Pck | Object PropertiEE |Freeze Sample Genr | She已t| Gnph | Stats 11血毗 |Augmented Dickey-Fuller Unit Root Test on CPIinu

24、yn lenieuunei iavi-ftJOTivnDependent Variable D(CPI)Method: Least SquaresDate: 06/13/12 Time: 1421Sample (adjusted): 19B1 2006Included observations: 26 after adjustmentsVanableCoefficientStd Errort* Stati sticProbCPK-1)0.0122180.0088401.3821490 1802D(CPI(-1)1.191B32Q.1777956.7034040.0000D(CPI(-2)-0.

25、5489910.105333-2.9621940 0070R-squared0.650090Mean dependent var6.424231Adjusted R-squared0.619663S.D. dependent var6.304869SE of regression5.121736kaike info criterion6.213031Sum squared： resid603.3400Schwarz criterion6.350196Log likelihood-7776940Hannan-Quinn criter.6254833DurbinWatson stat1 73625

26、2 - 一一图7可以看到伪概率 P =0.9541 ，在5%的水平下是接受有单位根的原假设的。 模型1的估计结果为：CPI t =0.0122 CPI 21.1918 CPI 2 0.549 CPIt -2综上所述，根据 ADF检验知，CPI序列存在单位根，即序列非平稳。3单整性检验所谓序列的单整性， 就是原序列经过d阶差分后变成了平稳序列，就称原序列为d阶单整序列。于是对序列的单整性检验又转化为平稳性检验，即可用ADF检验，其不同的就仅仅是需要对原序列进行差分。然后，对CPI进行单整性检验，跟上述的平稳的ADF检验步骤类似，只是在 Unit RootTest对话框的设置中选择 1st选项，就

27、是一阶差分，这小题的检验结果如下所示。对于模型3:Null Hypothesis: D(CPi) has a unit root Exogenous: Constant. LinearTrendLag Length: 1 (Automatic based on SIC, MAXLAG=6)t-StatisticProb.*Augmented Dickey*Fuller test statistic-3.1339070.1186Test critical values:1% level5% level10% level-4.356068 -3 595026-3.233456* MacKinnon

28、(1996) one-sided p values.Augmented Dickey-Fuller Test EquationDependent Variable D(CPL2)Method: Least SquaresDate: 06/13/12 Time: 14:24Sample (adjusted): 12006Included observations: 26 after adjustmentsDate: OS/13/12 Time: U:24Sample (adjusted): 1961 2006Included observations: 26 alter adjustmentsV

29、ariableCoefficientStd. Errort-StatisticProb.D(CPI(-1)*0.4069440.129645-3.1369070.0048D(CPI(-1)h2)0.5447200 1779363,0613320.0057C2.6504932.3797691.1137610 2774TREND(1978)-0.0067660.132002-0.0512580.9595R-squared0.394152Mean dependent var-0.012303Adjusted R-sqjared0.311536S.D dependentvar6 049997S.E.

30、of regression5.019825Akaike info criterion6.205306Sum squared resid5543702Schwarz criterion6.39&869Log likelihood-76.65897Hannan-Quinn criter.6 251042F-statistic477090BDurbin-Watson stat1755816ProbfF-statisti c)0.010399可以看到伪概率 P =0.1186 ，在5%的水平下是接受有单位根的原假设的。 模型3的估计结果为：-2 2二 CPI t = 2.650-0.0068

31、t - 0.407 LCPI t 丄 0.545 二 CPI t其中，趋势项参数 '的估计值的t统计量为t - -0.051258 ，查ADF分布临界值表得，模 型3样本个数为25个（最接近的个数）时1甌025 = 3.25，即接受0 =0的原假设，于是可与 进行模型2的估计。对于模型2 : Series: CPT Workfile: UNTTTLEDjiUrrtitledView|Pat|Object|Properties| PrintN日m皀Freeze Sample Genr | She皀t| Gph | Stats | IcJent|Augmented Dickey-Fulle

32、r Unit Root Test on D(CPI)Null Hypothesis: D(CPI) has a unit root Exogenous: ConstantLag Length: 1 Automatic based on SIC, MAXLAG=6)t-StaVsticProb*Augmented Dickey*Fuller test statistic-3.2168490.0304Test aitical values:1% level5% level10%le7el-3.711457-2.981038-2.629906* MacKinnon(1996) one-sided pvalues.Augmented Dicke