1、金融時(shí)間序列分析探究中國(guó)A股市場(chǎng)收益率的波動(dòng)情況基于GARCH模型第一部分 實(shí)驗(yàn)背景自1990年12月,我國(guó)建立了上海、深圳證券交易所,20多年來(lái),我國(guó)資本市場(chǎng)在拓寬融資渠道、促進(jìn)資本形成、優(yōu)化資源配置、分散市場(chǎng)風(fēng)險(xiǎn)方面發(fā)揮了不可替代的重要作用,有力推動(dòng)了實(shí)體經(jīng)濟(jì)的發(fā)展,成為我國(guó)市場(chǎng)經(jīng)濟(jì)的重要組成部分。自1980年第一次股票發(fā)行算起,我國(guó)股票市場(chǎng)歷經(jīng)30多年,就當(dāng)前的股票市場(chǎng)來(lái)看,股票市場(chǎng)的動(dòng)蕩和股票的突然瘋漲等一系列現(xiàn)象和問(wèn)題值得我們深入思考和深入研究。第二部分 實(shí)驗(yàn)分析目的及方法滬深300指數(shù)是在以上交所和深交所所有上市的股票中選取規(guī)模大流動(dòng)性強(qiáng)的最具代表性的300家成分股作為編制對(duì)象，成

2、為滬深證券所聯(lián)合開(kāi)發(fā)的第一個(gè)反應(yīng)A股市場(chǎng)整體走勢(shì)的指數(shù)。滬深300指數(shù)作為我國(guó)股票市場(chǎng)具有代表性的且作為股指期貨的標(biāo)的指數(shù)，以滬深300指數(shù)作為研究對(duì)象可以使得檢驗(yàn)結(jié)果更加具有真實(shí)性和完整性，較好的反應(yīng)我國(guó)股票市場(chǎng)的基本狀況。本文在檢驗(yàn)滬深300指數(shù)2011年1月4日到2012年12月12日的日收益率的相關(guān)時(shí)間序列特征的基礎(chǔ)上，對(duì)序列r建立條件異方差模型，并研究其收益波動(dòng)率。第三部分 實(shí)驗(yàn)樣本3.1數(shù)據(jù)來(lái)源數(shù)據(jù)來(lái)源于國(guó)泰安數(shù)據(jù)庫(kù)。3.2所選數(shù)據(jù)變量滬深300指數(shù)編制目標(biāo)是反映中國(guó)證券市場(chǎng)股票價(jià)格變動(dòng)的概貌和運(yùn)行狀況，并能夠作為投資業(yè)績(jī)的評(píng)價(jià)標(biāo)準(zhǔn)，為指數(shù)化投資和指數(shù)衍生產(chǎn)品創(chuàng)新提供基礎(chǔ)條件。故本

3、文選擇滬深300指數(shù)2011年1月4日到2012年12月12日的日收益率作為樣本，探究中國(guó)股票市場(chǎng)收益率的波動(dòng)情況。 第四部分 模型構(gòu)建4.1 單位根檢驗(yàn)觀察R的圖形，如下所示：圖4.2 R的柱狀統(tǒng)計(jì)圖 從滬深300指數(shù)收益率序列r的線性圖中，可觀察到對(duì)數(shù)收益率波動(dòng)的“集群”現(xiàn)象：波動(dòng)在一些時(shí)間段內(nèi)較小，在有的時(shí)間段內(nèi)較大。此外，由圖形可知，序列R沒(méi)有截距項(xiàng)且沒(méi)有趨勢(shì)，故選擇第三種形式?jīng)]有截距項(xiàng)且不存在趨勢(shì)進(jìn)行單位根檢驗(yàn)，檢驗(yàn)結(jié)果如下：表4.1 單位根檢驗(yàn)結(jié)果Null Hypothesis: R has a unit rootExogenous: NoneLag Length: 0 (Auto

4、matic - based on SIC, maxlag=21)t-StatisticProb.*Augmented Dickey-Fuller test statistic-31.292060.0000Test critical values:1% level-2.5673835% level-1.94115510% level-1.616476*MacKinnon (1996) one-sided p-values.單位根統(tǒng)計(jì)量ADF=31.29206小于臨界值，且P為0.0000，因此該序列不是單位根過(guò)程，即該序列是平穩(wěn)序列。圖4.2 R的正態(tài)分布檢驗(yàn)由圖可知，滬深300指數(shù)收益率序列均

5、值為0.010480，標(biāo)準(zhǔn)差為1.292140，偏度為0.164917，大于0，說(shuō)明序列分布有長(zhǎng)的右拖尾。峰度為4.828012，高于正態(tài)分布的峰度值3，說(shuō)明收益率序列具有尖峰和厚尾的特征。JB統(tǒng)計(jì)量為137.5854，P值為0.00000，拒絕該對(duì)數(shù)收益率序列服從正態(tài)分布的假設(shè)。其中右偏表明總體來(lái)說(shuō)，近年比較大的收益大多為正；尖峰厚尾表明有很多樣本值較大幅度偏離均值，即金融市場(chǎng)由于利多利空消息波動(dòng)較為劇烈，經(jīng)常大起大落，從而有很多比較大的正收益和負(fù)收益。4.2 檢驗(yàn)ARCH效應(yīng)首先觀察r的自相關(guān)圖，其結(jié)果如下：Date: 12/16/14 Time: 08:16Sample: 1 957In

6、cluded observations: 957AutocorrelationPartial CorrelationACPACQ-StatProb| | |1-0.011-0.0110.12440.724| | |20.0340.0341.25100.535| | |3-0.004-0.0041.27030.736| | |4-0.006-0.0081.30820.860| | |50.0290.0292.10910.834| | |6-0.039-0.0383.60350.730| | |70.0640.0617.57110.372| | |80.0130.0177.72480.461| |

7、 |90.0270.0238.41670.493| | |100.0520.05211.0730.352| | |110.0170.01911.3430.415| | |12-0.045-0.05313.3270.346| | |13-0.033-0.03114.4050.346| | |140.0350.03515.6300.336| | |150.0060.00515.6610.405| | |16-0.008-0.01215.7230.472| | |170.0080.00515.7920.539| | |180.0390.03417.2740.504| | |19-0.003-0.00

8、417.2810.571| | |20-0.029-0.02818.1120.580| | |21-0.020-0.02218.5180.616| | |220.0120.01818.6520.667| | |23-0.050-0.04621.0770.576| | |240.004-0.00121.0960.633| | |250.0110.00621.2050.681| | |26-0.016-0.01521.4460.719| | |270.0480.05023.7640.643| | |280.0500.05526.2550.559| | |29-0.025-0.03326.8860.

9、578*| | |30-0.066-0.05731.1450.408| | |31-0.0050.00431.1700.458| | |32-0.052-0.05833.8480.378| | |330.0130.01334.0070.419| | |34-0.049-0.04236.4010.358| | |35-0.025-0.03737.0240.376| | |360.0120.00637.1600.415圖4.3 R的自相關(guān)圖由自相關(guān)圖可知，該序列不存在自相關(guān)性。因此對(duì)R進(jìn)行常數(shù)回歸。其回歸結(jié)果如下：表4.2 回歸結(jié)果Dependent Variable: RMethod: Leas

10、t SquaresDate: 12/16/14 Time: 08:10Sample: 1 957Included observations: 957VariableCoefficientStd. Errort-StatisticProb.C0.0104800.0417690.2509050.8019R-squared0.000000Mean dependent var0.010480Adjusted R-squared0.000000S.D. dependent var1.292140S.E. of regression1.292140Akaike info criterion3.351521

11、Sum squared resid1596.162Schwarz criterion3.356603Log likelihood-1602.703Hannan-Quinn criter.3.353457Durbin-Watson stat2.020315由上表可知，對(duì)常數(shù)的回歸結(jié)果并不顯著。下面得到殘差平方的自相關(guān)圖：Date: 12/16/14 Time: 08:18Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationACPACQ-StatProb| | |10.0500.0502.37710.12

12、3|* |* |20.1070.10513.3800.001| | |30.0200.01013.7690.003| | |40.0350.02314.9580.005| | |50.0200.01415.3310.009| | |60.0310.02416.2710.012|* |* |70.0840.07823.0700.002| | |80.0150.00123.2780.003| | |90.0450.02725.2120.003| | |100.0610.05428.8180.001| | |110.014-0.00328.9990.002| | |120.0390.02530.49

13、20.002| | |130.0530.04433.2610.002| | |140.003-0.01833.2680.003| | |15-0.001-0.01433.2690.004| | |16-0.003-0.01133.2780.007| | |170.0200.01033.6570.009| | |180.0430.04135.4500.008| | |190.006-0.01035.4900.012| | |200.0320.01436.4860.013| | |210.0540.05239.3340.009| | |22-0.022-0.03939.8290.011| | |2

14、30.0140.00140.0120.015| | |24-0.047-0.04842.2160.012| | |250.0100.00342.3220.017| | |26-0.016-0.00942.5850.021| | |27-0.021-0.03043.0140.026| | |280.0250.02343.6420.030| | |29-0.037-0.03144.9790.030| | |300.0290.01945.7970.032| | |310.0230.03146.3430.038| | |320.0320.02747.3390.040| | |33-0.038-0.04

15、548.7650.038| | |340.0190.02249.1340.045| | |350.0250.03049.7340.051| | |360.0160.01849.9840.061圖4.4 殘差平方的自相關(guān)圖由上圖可知，殘差平方序列在滯后三階并不異于零，即存在自相關(guān)性，進(jìn)一步進(jìn)行l(wèi)m檢驗(yàn)，這里選取滯后將階數(shù)為3，檢驗(yàn)結(jié)果如下：表4.3 ARCH效應(yīng)檢驗(yàn)結(jié)果Heteroskedasticity Test: ARCHF-statistic4.373176Prob. F(3,950)0.0046Obs*R-squared12.99530Prob. Chi-Square(3)0.0046

16、由上表可知，p值為0.0046，因此在1%的顯著水平下是存在ARCH效應(yīng)的。選擇滯后階數(shù)更高的進(jìn)行檢驗(yàn),發(fā)現(xiàn)滯后4階也滿(mǎn)足在1%的顯著水平下存在ARCH效應(yīng)，再選取其他高階進(jìn)行檢驗(yàn)，發(fā)現(xiàn)高階殘差平方項(xiàng)均不滿(mǎn)足。4.3 模型的估計(jì)分別估計(jì)ARCH（2）、ARCH（1）和GARCH（1，1），由于R不存在自相關(guān)性，而且對(duì)常數(shù)回歸也不顯著，因此不對(duì)均值方程進(jìn)行設(shè)定，之設(shè)定方差方程。AECH（2）估計(jì)結(jié)果如下：表4.4 arch（2）模型的估計(jì)結(jié)果Dependent Variable: RMethod: ML - ARCH (Marquardt) - Normal distributionDate:

17、12/16/14 Time: 08:38Sample: 1 957Included observations: 957Convergence achieved after 8 iterationsPresample variance: backcast (parameter = 0.7)GARCH = C(1) + C(2)*RESID(-1)2 + C(3)*RESID(-2)2VariableCoefficientStd. Errorz-StatisticProb.Variance EquationC1.4099610.07656018.416520.0000RESID(-1)20.047

18、5310.0214202.2190530.0265RESID(-2)20.1062840.0239774.4328490.0000R-squared-0.000066Mean dependent var0.010480Adjusted R-squared0.000979S.D. dependent var1.292140S.E. of regression1.291507Akaike info criterion3.336256Sum squared resid1596.268Schwarz criterion3.351503Log likelihood-1593.399Hannan-Quin

19、n criter.3.342063Durbin-Watson stat2.020182 可以看出，殘差平方滯后項(xiàng)的系數(shù)在5%的顯著水平下都顯著，因此選擇arch（2）合適，再選擇ARCH(1)。表4.5 arch（1）模型的估計(jì)結(jié)果Dependent Variable: RMethod: ML - ARCH (Marquardt) - Normal distributionDate: 12/16/14 Time: 08:40Sample: 1 957Included observations: 957Convergence achieved after 7 iterationsPresampl

20、e variance: backcast (parameter = 0.7)GARCH = C(1) + C(2)*RESID(-1)2VariableCoefficientStd. Errorz-StatisticProb.Variance EquationC1.5948100.06252025.508840.0000RESID(-1)20.0432670.0207012.0901310.0366R-squared-0.000066Mean dependent var0.010480Adjusted R-squared0.000979S.D. dependent var1.292140S.E

21、. of regression1.291507Akaike info criterion3.350173Sum squared resid1596.268Schwarz criterion3.360337Log likelihood-1601.058Hannan-Quinn criter.3.354044Durbin-Watson stat2.020182 可以看出，殘差平方滯后項(xiàng)的系數(shù)在5%的顯著水平下顯著，因此選擇ARCH（1）合適。下面對(duì)GARCH（1，1）進(jìn)行估計(jì)。表4.6 GARCH（1，1）模型的估計(jì)結(jié)果Dependent Variable: RMethod: ML - ARCH

22、(Marquardt) - Normal distributionDate: 12/16/14 Time: 08:42Sample: 1 957Included observations: 957Convergence achieved after 9 iterationsPresample variance: backcast (parameter = 0.7)GARCH = C(1) + C(2)*RESID(-1)2 + C(3)*GARCH(-1)VariableCoefficientStd. Errorz-StatisticProb.Variance EquationC0.04637

23、30.0223702.0730260.0382RESID(-1)20.0383960.0091944.1762960.0000GARCH(-1)0.9348960.01941048.165150.0000R-squared-0.000066Mean dependent var0.010480Adjusted R-squared0.000979S.D. dependent var1.292140S.E. of regression1.291507Akaike info criterion3.326751Sum squared resid1596.268Schwarz criterion3.341

24、998Log likelihood-1588.850Hannan-Quinn criter.3.332558Durbin-Watson stat2.020182 以上模型的系數(shù)均滿(mǎn)足非負(fù)性，而且在5%的水平下顯著。 4.4模型殘差的檢驗(yàn)下面進(jìn)行殘差的自相關(guān)性的檢驗(yàn)，檢驗(yàn)結(jié)果如下：Date: 12/16/14 Time: 08:50Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationACPACQ-StatProb| | |10.0020.0020.00420.949| | |20.0200.0200.3

25、9500.821| | |3-0.006-0.0060.42600.935| | |4-0.011-0.0110.54150.969| | |50.0250.0251.14810.950| | |6-0.050-0.0503.57430.734| | |70.0620.0617.29700.399| | |80.0050.0077.32610.502| | |90.0220.0207.79880.555| | |100.0500.04910.1920.424| | |110.0110.01410.3130.502| | |12-0.041-0.04811.9260.452| | |13-0.0

26、38-0.03113.3050.425| | |140.0390.03814.7610.395| | |150.0090.00814.8320.464圖4.5 ARCH(2)模型殘差項(xiàng)的自相關(guān)圖Date: 12/16/14 Time: 08:51Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationACPACQ-StatProb| | |1-0.004-0.0040.01900.890| | |20.0320.0321.01080.603| | |3-0.005-0.0051.03510.793| |

27、|4-0.007-0.0091.08870.896| | |50.0280.0291.86690.867| | |6-0.039-0.0393.34970.764| | |70.0660.0647.56140.373| | |80.0120.0157.70170.463| | |90.0290.0258.50820.484| | |100.0550.05411.4800.321| | |110.0150.01711.6990.387| | |12-0.044-0.05313.6200.326| | |13-0.036-0.03214.8600.316| | |140.0340.03416.01

28、30.313| | |150.0050.00516.0400.379圖4.6 ARCH(1)模型殘差項(xiàng)的自相關(guān)圖Date: 12/16/14 Time: 08:52Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationACPACQ-StatProb| | |10.0100.0100.08940.765| | |20.0360.0361.31900.517| | |3-0.001-0.0011.31960.724| | |4-0.000-0.0011.31960.858| | |50.0300.0312.

29、21290.819| | |6-0.042-0.0423.89170.691| | |70.0600.0597.39280.389| | |80.0050.0067.41370.493| | |90.0270.0228.09450.525| | |100.0600.05911.6070.312| | |110.0140.01311.7860.380| | |12-0.044-0.05413.6300.325| | |13-0.033-0.02814.6930.327| | |140.0380.03816.0880.308| | |150.0040.00316.1000.375圖4.7 GARC

30、H(1,1)模型殘差項(xiàng)的自相關(guān)圖觀察殘差的自相關(guān)圖，可以看出均不存在自相關(guān)性。下面觀察殘差平方的自相關(guān)圖。Date: 12/16/14 Time: 08:53Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationACPACQ-StatProb| | |1-0.023-0.0230.52670.468| | |2-0.001-0.0020.52790.768| | |3-0.002-0.0020.53040.912| | |40.0020.0020.53330.970| | |50.0010.0010.5

31、3360.991| | |60.0250.0251.11770.981| | |70.0700.0715.88080.554| | |80.0010.0045.88150.660| | |90.0550.0568.85050.451| | |100.0690.07313.4890.198| | |110.0070.01113.5330.260| | |120.0250.02614.1220.293| | |130.0300.02914.9920.308| | |140.0070.00415.0390.376| | |15-0.005-0.00715.0620.447圖4.8 ARCH(2)模型

32、殘差平方的自相關(guān)圖Date: 12/16/14 Time: 08:54Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationACPACQ-StatProb| | |1-0.000-0.0000.00020.990|* |* |20.1090.10911.4110.003| | |30.0010.00111.4130.010| | |40.0270.01512.1010.017| | |50.0050.00512.1260.033| | |60.0280.02312.8620.045|* |* |70.0870.08720.1080.005| | |80.0100.00520.2120.010| | |90.0430.02521.9980.009| | |100.0630.06225.9050.004| | |110.005-0.00525.9290.007| | |120.04