金融计量学例题.doc

中国香港股市模型一、 研究目的研究中国香港股市变化规律，分析影响股价变动的主要因素。二、 影响因素分析被解释变量Y是香港恒生指数，影响因素主要从以下三个方面考虑：（1） 股票市场自身交易情况，用成交额X1（百万美元）综合反映。（2） 国民经济发展状况，除了反映经济发展水平的人均生产总值X2(现价美元）之外，由于不动产是香港投资上致富的主要源泉，房地产交易也是香港经济十分重要的组成部分，因此要考虑另外两个影响因素：建筑业总开支X3（百万美元）和房地产买卖金额X4（百万美元），以便分析整个国民经济以及各个重要组成部分的发展对香港股市的影响（3） 金融环境的变化，取九九金价X5（美元/两）、港汇指数x6、优惠利率X7等因素，从贵金属、汇率、利率等方面反映金融环境对香港股价波动的影响。恒生指数及其影响因素的统计资料恒生指数成交额人均生产总值建筑业总开支房地产买卖金额九九金价港汇指数利率yx1x2x3x4x5x6x71991172.91124610183411011242.5681105.991992352.941033510414399612693.94791107.46.51993447.6713115613134468916681.34607114.461994404.02612715033687622131.88714110.84.751995409.512741917389863631353.6491199.44.751996619.1725633217151233943528.81123191.19.519971121.1795684270751662370752.98276090.81019981506.841059873182719937125989.84265186.31619991105.7946230353932478799468.482105125.310.52000933.0337165388322511282478.33030107.410.520011008.5448787460792441454936.32810106.68.520021567.5675808478712297087135.512649115.7620031960.061231285437224403129884.033031110.16.520042884.883714066560230531163044.23644105.8520052556.721985697491737861215033.623690101.65.25三、 多重共线性分析可用逐步回归法进行变量选择Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:07Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C493.6722158.53633.1139370.0082X10.0073370.0012445.8958090.0001R-squared0.727809 Mean dependent var1136.720Adjusted R-squared0.706871 S.D. dependent var823.0463S.E. of regression445.6086 Akaike info criterion15.16032Sum squared resid2581372. Schwarz criterion15.25473Log likelihood-111.7024 F-statistic34.76056Durbin-Watson stat1.327326 Prob(F-statistic)0.000053Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:09Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C-147.2516151.9300-0.9692070.3501X20.0377760.0038659.7739500.0000R-squared0.880218 Mean dependent var1136.720Adjusted R-squared0.871004 S.D. dependent var823.0463S.E. of regression295.6060 Akaike info criterion14.33950Sum squared resid1135978. Schwarz criterion14.43390Log likelihood-105.5462 F-statistic95.53011Durbin-Watson stat1.389152 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:09Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C-80.15322211.5083-0.3789600.7108X30.0682910.0102946.6340630.0000R-squared0.771973 Mean dependent var1136.720Adjusted R-squared0.754432 S.D. dependent var823.0463S.E. of regression407.8587 Akaike info criterion14.98328Sum squared resid2162534. Schwarz criterion15.07769Log likelihood-110.3746 F-statistic44.01080Durbin-Watson stat1.022370 Prob(F-statistic)0.000016Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:10Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C133.3664117.58101.1342510.2772X40.0129040.00120910.670620.0000R-squared0.897526 Mean dependent var1136.720Adjusted R-squared0.889644 S.D. dependent var823.0463S.E. of regression273.4151 Akaike info criterion14.18342Sum squared resid971825.5 Schwarz criterion14.27783Log likelihood-104.3757 F-statistic113.8620Durbin-Watson stat1.716793 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:10Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C-194.0396220.6236-0.8795050.3951X50.6376420.0934736.8217020.0000R-squared0.781643 Mean dependent var1136.720Adjusted R-squared0.764847 S.D. dependent var823.0463S.E. of regression399.1167 Akaike info criterion14.93995Sum squared resid2070823. Schwarz criterion15.03436Log likelihood-110.0496 F-statistic46.53562Durbin-Watson stat0.974820 Prob(F-statistic)0.000012Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:11Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C1482.4772347.4990.6315140.5387X6-3.28541622.20766-0.1479410.8847R-squared0.001681 Mean dependent var1136.720Adjusted R-squared-0.075113 S.D. dependent var823.0463S.E. of regression853.3975 Akaike info criterion16.45989Sum squared resid9467734. Schwarz criterion16.55430Log likelihood-121.4492 F-statistic0.021886Durbin-Watson stat0.215522 Prob(F-statistic)0.884660Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:12Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C1337.975621.34162.1533640.0506X7-25.4216373.42366-0.3462320.7347R-squared0.009137 Mean dependent var1136.720Adjusted R-squared-0.067083 S.D. dependent var823.0463S.E. of regression850.2046 Akaike info criterion16.45240Sum squared resid9397021. Schwarz criterion16.54680Log likelihood-121.3930 F-statistic0.119877Durbin-Watson stat0.246059 Prob(F-statistic)0.734708从上述7个表可以看出，以X4为解释变量时，R2最大，但常数项不显著，就把不含常数项含X4的一元线性回归模型作为基本模型（所有不含常数项的一元线性回归模型中，此模型R2最大）在此基础上分别加入X1,X2,X3,X5,X6,X7Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:21Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0105980.0010619.9880420.0000X10.0030000.0008103.7042670.0026R-squared0.945213 Mean dependent var1136.720Adjusted R-squared0.940999 S.D. dependent var823.0463S.E. of regression199.9192 Akaike info criterion13.55727Sum squared resid519580.1 Schwarz criterion13.65168Log likelihood-99.67952 F-statistic224.2834Durbin-Watson stat1.190080 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:22Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0076980.0024483.1453420.0077X20.0161010.0060542.6594770.0197R-squared0.927066 Mean dependent var1136.720Adjusted R-squared0.921456 S.D. dependent var823.0463S.E. of regression230.6650 Akaike info criterion13.84338Sum squared resid691682.2 Schwarz criterion13.93778Log likelihood-101.8253 F-statistic165.2434Durbin-Watson stat1.886847 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:26Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0114130.0029143.9163650.0018X30.0126560.0137910.9177170.3755R-squared0.894237 Mean dependent var1136.720Adjusted R-squared0.886102 S.D. dependent var823.0463S.E. of regression277.7686 Akaike info criterion14.21502Sum squared resid1003020. Schwarz criterion14.30943Log likelihood-104.6126 F-statistic109.9165Durbin-Watson stat1.648368 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:27Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0101460.0022494.5112360.0006X50.1666240.0926481.7984690.0954R-squared0.909822 Mean dependent var1136.720Adjusted R-squared0.902885 S.D. dependent var823.0463S.E. of regression256.4876 Akaike info criterion14.05560Sum squared resid855216.8 Schwarz criterion14.15001Log likelihood-103.4170 F-statistic131.1597Durbin-Watson stat1.546147 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:28Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0128740.00118010.913160.0000X61.3100601.0851081.2073090.2488R-squared0.898739 Mean dependent var1136.720Adjusted R-squared0.890950 S.D. dependent var823.0463S.E. of regression271.7927 Akaike info criterion14.17152Sum squared resid960326.4 Schwarz criterion14.26593Log likelihood-104.2864 F-statistic115.3811Durbin-Watson stat1.726650 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:28Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0139300.00116811.927170.0000X71.06294513.419740.0792080.9381R-squared0.887440 Mean dependent var1136.720Adjusted R-squared0.878781 S.D. dependent var823.0463S.E. of regression286.5559 Akaike info criterion14.27731Sum squared resid1067486. Schwarz criterion14.37172Log likelihood-105.0798 F-statistic102.4936Durbin-Watson stat1.705970 Prob(F-statistic)0.000000以X4、X1为解释变量的模型为基本回归模型，在此基础上分别加入x2、x3、x5、x6、x7得Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:33Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0052660.0015403.4200070.0051X10.0027760.0005604.9568020.0003X20.0142720.0036283.9332800.0020R-squared0.976068 Mean dependent var1136.720Adjusted R-squared0.972079 S.D. dependent var823.0463S.E. of regression137.5281 Akaike info criterion12.86239Sum squared resid226967.8 Schwarz criterion13.00400Log likelihood-93.46793 F-statistic244.7054Durbin-Watson stat1.836293 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:34Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0059030.0021292.7726420.0169X10.0033490.0007044.7557460.0005X30.0210250.0086332.4356130.0314R-squared0.963337 Mean dependent var1136.720Adjusted R-squared0.957227 S.D. dependent var823.0463S.E. of regression170.2195 Akaike info criterion13.28891Sum squared resid347696.2 Schwarz criterion13.43052Log likelihood-96.66683 F-statistic157.6545Durbin-Watson stat1.544291 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:34Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0065790.0015604.2183580.0012X10.0030370.0006334.7956870.0004X50.1718860.0564763.0435390.0102R-squared0.969081 Mean dependent var1136.720Adjusted R-squared0.963927 S.D. dependent var823.0463S.E. of regression156.3193 Akaike info criterion13.11854Sum squared resid293228.8 Schwarz criterion13.26015Log likelihood-95.38901 F-statistic188.0534Durbin-Watson stat1.625470 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:36Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0094260.0011688.0669160.0000X10.0030150.0007464.0437940.0016X61.3428930.7348141.8275290.0926R-squared0.957142 Mean dependent var1136.720Adjusted R-squared0.949999 S.D. dependent var823.0463S.E. of regression184.0414 Akaike info criterion13.44505Sum squared resid406454.9 Schwarz criterion13.58667Log likelihood-97.83791 F-statistic133.9960Durbin-Watson stat1.251355 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:36Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0097920.0013597.2027090.0000X10.0031750.0008333.8106950.0025X79.1844879.6341420.9533270.3592R-squared0.949070 Mean dependent var1136.720Adjusted R-squared0.940582 S.D. dependent var823.0463S.E. of regression200.6240 Akaike info criterion13.61760Sum squared resid482999.7 Schwarz criterion13.75921Log likelihood-99.13199 F-statistic111.8097Durbin-Watson stat1.285437 Prob(F-statistic)0.000000以X1 、X2 、X4为解释变量的模型为基本模型，在此基础上再加入 X3、X5、X6、X7Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:44Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0060480.0017183.5206350.0048X10.0024100.0006643.6271670.0040X20.0213430.0078222.7285400.0196X3-0.0153370.015036-1.0200050.3296R-squared0.978136 Mean dependent var1136.720Adjusted R-squared0.972172 S.D. dependent var823.0463S.E. of regression137.2971 Akaike info criterion12.90535Sum squared resid207355.5 Schwarz criterion13.09416Log likelihood-92.79013 F-statistic164.0331Durbin-Watson stat1.825783 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:45Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0051320.0015883.2324800.0080X10.0028350.0005794.8916190.0005X20.0112660.0057731.9514980.0769X50.0537410.0790560.6797780.5107R-squared0.977032 Mean dependent var1136.720Adjusted R-squared0.970768 S.D. dependent var823.0463S.E. of regression140.7181 Akaike info criterion12.95457Sum squared resid217817.5 Schwarz criterion13.14339Log likelihood-93.15930 F-statistic155.9783Durbin-Watson stat1.855979 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:46Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0051960.0016973.0612640.0108X10.0027680.0005874.7124790.0006X20.0146840.0049702.9543520.0131X6-0.0962920.752157-0.1280210.9004R-squared0.976103 Mean dependent var1136.720Adjusted R-squared0.969586 S.D. dependent var823.0463S.E. of regression143.5365 Akaike info criterion12.99423Sum squared resid226630.1 Schwarz criterion13.18305Log likelihood-93.45676 F-statistic149.7704Durbin-Watson stat1.846252 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 12/20/09 Time: 22:46Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. X40.0052560.0016143.2569350.0076X10.0027870.0006074.5954170.0008X20.0141740.0040223.5241740.0048X70.5313617.3203050.0725870.9434R-squared0.976079 Mean dependent var1136.720Adjusted R-squared0.969555 S.D. dependent var823.0463S.E. of regression143.6090 Akaike info criterion12.99524Sum squared resid226859.1 Schwarz criterion13.18406Log likelihood-93.46434 F-statistic149.6156Durbin-Watson stat1.837869 Prob(F-statistic)0.000000经过变量选择后，解释变量中保留X1、X2、 X4四、 进行异方差性检验White Heteroskedasticity Test:F-statistic2.869605 Probability0.129119Obs*R-squared12.56702 Probability0.183196Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/20/09 Time: 22:49Sample: 1974 1988Included observations: 15VariableCoefficientStd. Errort-StatisticProb. C92911.1547840.041.9421210.1098X10.7082750.2561992.7645560.0396X122.97E-061.78E-061.6712410.1555X1*X2-8.76E-054.77E-05-1.8364070.1257X1*X41.95E-051.35E-051.4411930.2091X2-13.416697.015781-1.9123580.1140X220.0002270.0001241.8261430.1274X2*X44.00E-053.30E-051.2144170.2788X42.6052621.5707961.6585620.1581X42-2.84E-051.40E-05-2.0312010.0980R-squared0.837802 Mean dependent var15131.19Adjusted R-squared0.545844 S.D. dependent var15156.98S.E. of regression10214.45 Akaike info criterion21.53572Sum squared resid5.22E+08 Schwarz criterion22.00775Log likelihood-151.5179 F-statistic2.869605Durbin-Watson stat2.661580 Prob(F-statistic)0.129119给定显著水平=0.05,2=16.919,2=12.567知随机项具有等方差性。五、 检验自相关性用布罗斯格弗雷检验（或LM）Breusch-Godfrey Serial Correlation LM Test:F-statistic4.160204 Probability0.041124Obs*R-squared10.12966 Probability0.038299Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/20/09 Time: 23:11VariableCoefficientStd. Errort-StatisticProb. X15.58E-050.0005300.1053020.9187X2-0.0042260.003836-1.1016500.3027X40.0020170.00148