eviews期中作业报告(要点：基本统计和OLS、稳健方差).docx

Eviews期中实验报告一、 实验任务上机内容：基本统计和OLS、稳健方差 要点 描述性统计 简单假设检验 季节调整：移动平均法 多元统计分析：齐性检验；主成分分析 方程对象：方程设定，估计结果，系数，成员函数 方差稳健估计：HC和HAC 哑变量和交互项二、 实验内容1. 简单统计分析与描述性统计数据查看：m1.sheetm1StatsM1Mean378.1643Median274.0275Maximum1089.475Minimum129.8910Std. Dev.265.4934Skewness1.012404Kurtosis2.765155Jarque-Bera27.70001Probability0.000001Sum60506.30Sum Sq. Dev.11207393Observations160从而显示出了m1的各种统计信息，包括均值，中位点，最大值最小值，以及二到四阶矩观测数目和正态分布检验等的统计概要。M1.line则显示出了这一组数据的图形描述freeze(gk) G(1).distplot kernel G(1).kdensityV6 - G(1).distplot kernel画出对象g中第一个变量的直方图，命名为ghfreeze(gh) G(1).histhist log(m1)将g中的所有变量画入一张线性图中，改图命名为gfagraph gfa.line G将g中所有的变量分别画出一张图并合并入gfg这一个对象中graph gfg.line(m) Gmultiple graphs生成列表tbgsi，该列表中包含了g中所有变量单独的统计值freeze(tbGsi) G.stats(i)individual samples回归模型估计smpl 1952Q1 1992Q4equation eq1.ls log(m1) c log(gdp) rs dlog(pr)Dependent Variable: LOG(M1)Method: Least SquaresDate: 12/07/12 Time: 15:41Sample (adjusted): 1952Q2 1992Q4Included observations: 163 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C1.3123830.03219940.758500.0000LOG(GDP)0.7720350.006537118.10920.0000RS-0.0206860.002516-8.2211960.0000DLOG(PR)-2.5722040.942556-2.7289670.0071R-squared0.993274Mean dependent var5.692279Adjusted R-squared0.993147S.D. dependent var0.670253S.E. of regression0.055485Akaike info criterion-2.921176Sum squared resid0.489494Schwarz criterion-2.845256Log likelihood242.0759Hannan-Quinn criter.-2.890354F-statistic7826.904Durbin-Watson stat0.140967Prob(F-statistic)0.000000这里我们使用smpl来设定估计样本的观测区间，而equation语句则创建了方程对象eq1并进行最小二乘估计，其中的c代表回归方程的常数项，得到模型估计的结果如上图所示。freeze(gfeq1r) eq1.resids这里我们产生了残差项的图使用表格来查看残差，命令为：eq.Resids（t）另外我们可以查看回归结果的文本表示：eq1.representationsEstimation Command:=LS LOG(M1) C LOG(GDP) RS DLOG(PR)Estimation Equation:=LOG(M1) = C(1) + C(2)*LOG(GDP) + C(3)*RS + C(4)*DLOG(PR)Substituted Coefficients:=LOG(M1) = 1.31238347449 + 0.772034899215*LOG(GDP) - 0.0206860343222*RS - 2.57220371427*DLOG(PR)接下来我们来对这一结果进行假设检验。进行wald检验，检验b4=2是否成立，命令为：Eq1.wald c(4)=2Wald Test:Equation: EQ1Test StatisticValuedfProbabilityF-statistic23.53081(1, 159)0.0000Chi-square23.5308110.0000Null Hypothesis Summary:Normalized Restriction (= 0)ValueStd. Err.-2 + C(4)-4.5722040.942556Restrictions are linear in coefficients.从而我们看到这一假设被拒绝了，下面我们进行序列相关检验，命令如下：eq1.auto(1)Breusch-Godfrey Serial Correlation LM Test:F-statistic813.0060Prob. F(1,158)0.0000Obs*R-squared136.4770Prob. Chi-Square(1)0.0000Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/07/12 Time: 15:49Sample: 1952Q2 1992Q4Included observations: 163Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C-0.0063550.013031-0.4876830.6265LOG(GDP)0.0009970.0026450.3769290.7067RS-0.0005670.001018-0.5567480.5785DLOG(PR)0.4041430.3816761.0588640.2913RESID(-1)0.9203060.03227628.513260.0000R-squared0.837282Mean dependent var4.92E-16Adjusted R-squared0.833163S.D. dependent var0.054969S.E. of regression0.022452Akaike info criterion-4.724644Sum squared resid0.079649Schwarz criterion-4.629744Log likelihood390.0585Hannan-Quinn criter.-4.686116F-statistic203.2515Durbin-Watson stat1.770965Prob(F-statistic)0.000000接下来我们要进行模型的修改，调整季节性，采用移动平均法equation eq2.ls log(m1) c log(gdp) rs dlog(pr) log(m1(-1) log(gdp(-1) rs(-1) dlog(pr(-1)Dependent Variable: LOG(M1)Method: Least SquaresDate: 12/07/12 Time: 15:52Sample (adjusted): 1952Q3 1992Q4Included observations: 162 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C0.0712970.0282482.5239490.0126LOG(GDP)0.3203380.1181862.7104530.0075RS-0.0052220.001469-3.5548010.0005DLOG(PR)0.0386150.3416190.1130360.9101LOG(M1(-1)0.9266400.02031945.603750.0000LOG(GDP(-1)-0.2573640.123264-2.0879100.0385RS(-1)0.0026040.0015741.6544290.1001DLOG(PR(-1)-0.0716500.347403-0.2062460.8369R-squared0.999604Mean dependent var5.697490Adjusted R-squared0.999586S.D. dependent var0.669011S.E. of regression0.013611Akaike info criterion-5.707729Sum squared resid0.028531Schwarz criterion-5.555255Log likelihood470.3261Hannan-Quinn criter.-5.645823F-statistic55543.30Durbin-Watson stat2.393764Prob(F-statistic)0.000000equation eq2.ls log(m1) c log(gdp) rs dlog(pr)Dependent Variable: LOG(M1)Method: Least SquaresDate: 12/07/12 Time: 15:53Sample (adjusted): 1952Q2 1992Q4Included observations: 163 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C1.3123830.03219940.758500.0000LOG(GDP)0.7720350.006537118.10920.0000RS-0.0206860.002516-8.2211960.0000DLOG(PR)-2.5722040.942556-2.7289670.0071R-squared0.993274Mean dependent var5.692279Adjusted R-squared0.993147S.D. dependent var0.670253S.E. of regression0.055485Akaike info criterion-2.921176Sum squared resid0.489494Schwarz criterion-2.845256Log likelihood242.0759Hannan-Quinn criter.-2.890354F-statistic7826.904Durbin-Watson stat0.140967Prob(F-statistic)0.000000从而看出之后模型和自回归模型的拟合效果大致相当，而信息准则表明，之后模型略好，因为之后模型的AIC值和sc值都比较小。2. OLSEquation eq01.ls gdp c m1建立了方程对象eq01，将模型设定为：GDP=B1+B2*M1+E的线性回归模型，c表示常数项，并且使用普通最小二乘法进行估计Freeze(txEq) eq01.representations将方程对象eq01的表示试图定格成文本对象，文本表示信息如图所示：Estimation Command:=LS GDP C M1Estimation Equation:=GDP = C(1) + C(2)*M1Substituted Coefficients:=GDP = -92.2429670327 + 1.62843028117*M1freeze(tb01) eq01.output查看详细的估计结果Dependent Variable: GDPMethod: Least SquaresDate: 12/04/12 Time: 16:18Sample: 1952Q1 1996Q4Included observations: 180VariableCoefficientStd. Errort-StatisticProb.C-92.242976.751931-13.661720.0000M11.6284300.012006135.63640.0000R-squared0.990417Mean dependent var632.4190Adjusted R-squared0.990364S.D. dependent var564.2441S.E. of regression55.38936Akaike info criterion10.87770Sum squared resid546100.6Schwarz criterion10.91318Log likelihood-976.9931Hannan-Quinn criter.10.89209F-statistic18397.24Durbin-Watson stat0.077568Prob(F-statistic)0.000000首先我们从表头可以看出，在此次统计结果中，因变量为gdp，使用的回归方法为最小二乘法，sample的时间是从1952年的第一季度到1996年的第四季度，总共的观测值为180个。可以看到常数项为-92.24297，斜率为1.628430二者的标准差分别为6.751931和0.012006从而可以看出在此案例中对于斜率来说Ols估计的更好。对于p-value我们也可以看出其值基本为0，从而可以接受原假设。之后的参数R-squred表明了解释变量与原变量之间有很强的正相关关系。使用resids命令产生残差估计的图形视图Coefcov报告系数估计的协方差矩阵CM1C45.5885680269021-0.06414340641355956M1-0.064143406413559560.00014414040429454373. 方差的稳健估计m1 realgdp cpi_upagestruct(freq=q,start=1950q1)equation eq01.ls log(m1) c log(realgdp) log(cpi_u)graph gf.line residge.axis zerolinegf.axis zerolinegf.legend -display生成了关于realgdp 和cpi的log回归模型的残差值和各个参数的估计值Dependent Variable: LOG(M1)Method: Least SquaresDate: 12/04/12 Time: 16:55Sample: 1950Q1 2000Q4Included observations: 204VariableCoefficientStd. Errort-StatisticProb.C-1.6330570.228568-7.1447270.0000LOG(REALGDP)0.2870510.0473846.0579570.0000LOG(CPI_U)0.9718120.03377328.774880.0000R-squared0.989520Mean dependent var5.797855Adjusted R-squared0.989415S.D. dependent var0.805567S.E. of regression0.082878Akaike info criterion-2.128286Sum squared resid1.380637Schwarz criterion-2.079491Log likelihood220.0852Hannan-Quinn criter.-2.108548F-statistic9488.775Durbin-Watson stat0.024767Prob(F-statistic)0.000000我们可以看出这个残差某种程度上带有一定的规律，也即一定的趋势和季节性，从而我们要对轨迹的标准差进行修正。equation eq02.ls(n) log(m1) c log(realgdp) log(cpi_u)for !i=1 to 3tb(!i +1,2) = eq01.c(!i)tb(!i+1,3) = eq01.stderrs(!i)tb(!i+1,4) = eq02.stderrs(!i)nexttb(1,1)=variabletb(1,2)=ols estimatetb(1,3)=ols setb(1,4)=corrected setb(2,1)=constanttb(3,1)=in outputtb(4,1)=in cpitb.setformat(2,2,4,4) f.5variableols estimateols secorrected seconstant-1.633060.228570.31389in output0.287050.047380.07286in cpi0.971810.033770.06127freeze(tb02) eq02.outputtb02.settextcolor(6,1) blue生成关于第二个估计模型的参数估计与统计信息Dependent Variable: LOG(M1)Method: Least SquaresDate: 12/04/12 Time: 17:03Sample: 1950Q1 2000Q4Included observations: 204Newey-West HAC Standard Errors & Covariance (lag truncation=4)VariableCoefficientStd. Errort-StatisticProb.C-1.6330570.313889-5.2026590.0000LOG(REALGDP)0.2870510.0728573.9399240.0001LOG(CPI_U)0.9718120.06127415.860160.0000R-squared0.989520Mean dependent var5.797855Adjusted R-squared0.989415S.D. dependent var0.805567S.E. of regression0.082878Akaike info criterion-2.128286Sum squared resid1.380637Schwarz criterion-2.079491Log likelihood220.0852Hannan-Quinn criter.-2.108548F-statistic9488.775Durbin-Watson stat0.024767Prob(F-statistic)0.000000从蓝体的文字可以看出来标准差和方差修正为Newey-West HAC估计，并且L为4。从这个表格和上一次未经过方差修正的表格可以看出这之中我们在使用white HC估计或者Newey-West HAC估计进行修正的时候，并没有改变系数的点估计值，仅仅只是修正了估计的标准差。4.哑变量与交互项哑变量表示这个变量的值只为1或者0两个值也即描述定性信息的变量学生是否有笔记本电脑，作业是否完成等等。当在回归分析中，全部解释变量为哑变量的时候，这就是方差分析。当哑变量的值取为1的时候，表示属于某一类或者选择某一种行动。考虑如下两个变量：1) Sex：取值为1和0，代表男和女2) Nation：取名为cn，fr和us表示中国、法国和美国从而如下语句expand（sex，nation）将产生6个哑变量Category sexnation10cn20fr30us41cn51fr61usexpand(sex)将产生两个哑变量，期中对用于男性分组的哑变量，取值上等于序列sex的值expand(nation)将产生三个哑变量。expand产生的哑变量组是正交完全组（即任意的参数序列可以使数值序列获字符串序列）expand的参数序列有多个时，交叉分组得到n个组，就产生了n个哑变量，因此使用时要很小心，否则可能产生几多的哑变量。5.假设检验group g m1 gdpg.linefit(y1,xb=-0.5)g.linefit(yl,xb=-0.5)g.scat linefit(yl,xb=-0.5)这里我们将吗m1和gdp作为一组并且用曲线去拟合，这之中我们对y做了对数变换，对x做了box-cox变换，可以看出图像如上图所示。对于模型选择，我们应当注意：1) 简约型：模型要尽可能简单2) 可识别性：参数的估计值是惟一的3) 拟合优度：解释因变量变化的能力4) 一致性：和理论或者直觉一致5) 预测能力：样本预测的准确性smpl 1952Q1 1992Q4equation eq01.ls log(m1) c log(gdp) rs dlog(pr)freeze(gf) eq01.cellipse c(1), c(2),c(3)从而我们得到了三个置信椭圆，其中的虚线给出了单个系数的置信区间，默认的置信水平为95%。这里出现椭圆的原因主要是由于相关性导致的，其中c（1）和c（2）是高度负相关的，如果两者独立则置信椭圆应该为一个圆。Wald检验这里使用的模型是log(VALUEADD)=b1+b2*log(LABOR)+b3*log(CAPITAL)+e来估计cobb-douglas生产函数。equation eq01.ls log(ValueAdd) c log(Labor) log(Capital)Dependent Variable: LOG(VALUEADD)Method: Least SquaresDate: 12/07/12 Time: 15:12Sample: 1 25Included observations: 25VariableCoefficientStd. Errort-StatisticProb.C1.8444160.2335937.8958570.0000LOG(LABOR)0.8051830.1263346.3734660.0000LOG(CAPITAL)0.2454280.1068572.2967810.0315R-squared0.973075Mean dependent var5.812092Adjusted R-squared0.970627S.D. dependent var1.375304S.E. of regression0.235706Akaike info criterion0.059703Sum squared resid1.222260Schwarz criterion0.205968Log likelihood2.253715Hannan-Quinn criter.0.100271F-statistic397.5427Durbin-Watson stat1.957550Prob(F-statistic)0.000000eq01.wald c(2)+c(3)=1Wald Test:Equation: EQ01Test StatisticValuedfProbabilityF-statistic1.540692(1, 22)0.2276Chi-square1.54069210.2145Null Hypothesis Summary:Normalized Restriction (= 0)ValueStd. Err.-1 + C(2) + C(3)0.0506110.040774Restrictions are linear in coefficients.从而得到wald检验的结果同时我们也可以添加多个限制条件来进行wald检验如：eq01.wald c(2)=2/3,c(3)=1/3Wald Test:Equation: EQ01Test StatisticValuedfProbabilityF-statistic0.865866(2, 22)0.4345Chi-square1.73173120.4207Null Hypothesis Summary:Normalized Restriction (= 0)ValueStd. Err.-2/3 + C(2)0.1385160.126334-1/3 + C(3)-0.0879050.106857Restrictions are linear in coefficients.对于遗漏变量的处理，命令testadd可以用来检验是否存在遗漏变量。Testadd的零假设是增加的那些变量作为一个整体没有显著的贡献。smpl 1953Q1 1992Q4equation eq1.ls log(m1) c log(gdp)eq1.testadd rs dlog(pr)Omitted Variables: RS DLOG(PR)F-statistic86.18047Prob. F(2,156)0.0000Log likelihood ratio119.0812Prob. Chi-Square(2)0.0000Test Equation:Dependent Variable: LOG(M1)Method: Least SquaresDate: 12/07/12 Time: 15:24Sample: 1953Q1 1