1、金融時間序列分析探究中國A股市場收益率的波動情況基于GARCH模型第一部分 實驗背景自1990年12月,我國建立了上海、深圳證券交易所,20多年來,我國資本市場在拓寬融資渠道、促進資本形成、優化資源配置、分散市場風險方面發揮了不可替代的重要作用,有力推動了實體經濟的發展,成為我國市場經濟的重要組成部分。自1980年第一次股票發行算起,我國股票市場歷經30多年,就當前的股票市場來看,股票市場的動蕩和股票的突然瘋漲等一系列現象和問題值得我們深入思考和深入研究。第二部分 實驗分析目的及方法滬深300指數是在以上交所和深交所所有上市的股票中選取規模大流動性強的最具代表性的300家成分股作為編制對象，成

2、為滬深證券所聯合開發的第一個反應A股市場整體走勢的指數。滬深300指數作為我國股票市場具有代表性的且作為股指期貨的標的指數，以滬深300指數作為研究對象可以使得檢驗結果更加具有真實性和完整性，較好的反應我國股票市場的基本狀況。本文在檢驗滬深300指數2011年1月4日到2012年12月12日的日收益率的相關時間序列特征的基礎上，對序列r建立條件異方差模型，并研究其收益波動率。第三部分 實驗樣本3.1數據來源數據來源于國泰安數據庫。3.2所選數據變量滬深300指數編制目標是反映中國證券市場股票價格變動的概貌和運行狀況，并能夠作為投資業績的評價標準，為指數化投資和指數衍生產品創新提供基礎條件。故本

3、文選擇滬深300指數2011年1月4日到2012年12月12日的日收益率作為樣本，探究中國股票市場收益率的波動情況。 第四部分 模型構建4.1 單位根檢驗觀察R的圖形，如下所示：圖4.2 R的柱狀統計圖 從滬深300指數收益率序列r的線性圖中，可觀察到對數收益率波動的“集群”現象：波動在一些時間段內較小，在有的時間段內較大。此外，由圖形可知，序列R沒有截距項且沒有趨勢，故選擇第三種形式沒有截距項且不存在趨勢進行單位根檢驗，檢驗結果如下：表4.1 單位根檢驗結果Null Hypothesis: R has a unit rootExogenous: NoneLag Length: 0 (Auto

4、matic - based on SIC, maxlag=21)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-31.29206 0.0000Test critical values:1% level-2.5673835% level-1.94115510% level-1.616476*MacKinnon (1996) one-sided p-values.單位根統計量ADF=31.29206小于臨界值，且P為 0.0000，因此該序列不是單位根過程，即該序列是平穩序列。圖4.2 R的

5、正態分布檢驗由圖可知，滬深300指數收益率序列均值為0.010480，標準差為1.292140，偏度為0.164917，大于0，說明序列分布有長的右拖尾。峰度為4.828012，高于正態分布的峰度值3，說明收益率序列具有尖峰和厚尾的特征。JB統計量為137.5854，P值為0.00000，拒絕該對數收益率序列服從正態分布的假設。其中右偏表明總體來說，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，即金融市場由于利多利空消息波動較為劇烈，經常大起大落，從而有很多比較大的正收益和負收益。4.2 檢驗ARCH效應首先觀察r的自相關圖，其結果如下：Date: 12/16/14 Ti

6、me: 08:16Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationAC  PAC Q-Stat Prob        | |        | |1-0.011-0.0110.12440.724        | |&#

7、160;       | |20.0340.0341.25100.535        | |        | |3-0.004-0.0041.27030.736        | |        | |4

8、-0.006-0.0081.30820.860        | |        | |50.0290.0292.10910.834        | |        | |6-0.039-0.0383.60350.730    

9、60;   | |        | |70.0640.0617.57110.372        | |        | |80.0130.0177.72480.461        | |    

10、0;   | |90.0270.0238.41670.493        | |        | |100.0520.05211.0730.352        | |        | |110.0170.01911.3430.415 

11、;       | |        | |12-0.045-0.05313.3270.346        | |        | |13-0.033-0.03114.4050.346        | |

12、        | |140.0350.03515.6300.336        | |        | |150.0060.00515.6610.405        | |        |

13、|16-0.008-0.01215.7230.472        | |        | |170.0080.00515.7920.539        | |        | |180.0390.03417.2740.504    

14、    | |        | |19-0.003-0.00417.2810.571        | |        | |20-0.029-0.02818.1120.580        | |   &

15、#160;    | |21-0.020-0.02218.5180.616        | |        | |220.0120.01818.6520.667        | |        | |23-0.050-0.04621

16、.0770.576        | |        | |240.004-0.00121.0960.633        | |        | |250.0110.00621.2050.681      

17、0; | |        | |26-0.016-0.01521.4460.719        | |        | |270.0480.05023.7640.643        | |      &

18、#160; | |280.0500.05526.2550.559        | |        | |29-0.025-0.03326.8860.578       *| |        | |30-0.066-0.05731.1450.408  &#

19、160;     | |        | |31-0.0050.00431.1700.458        | |        | |32-0.052-0.05833.8480.378        | | 

20、0;      | |330.0130.01334.0070.419        | |        | |34-0.049-0.04236.4010.358        | |        | |35-0.02

21、5-0.03737.0240.376        | |        | |360.0120.00637.1600.415圖4.3 R的自相關圖由自相關圖可知，該序列不存在自相關性。因此對R進行常數回歸。其回歸結果如下：表4.2 回歸結果Dependent Variable: RMethod: Least SquaresDate: 12/16/14 Time: 08:10Sample: 1 957Included observati

22、ons: 957VariableCoefficientStd. Errort-StatisticProb.  C0.0104800.0417690.2509050.8019R-squared0.000000    Mean dependent var0.010480Adjusted R-squared0.000000    S.D. dependent var1.292140S.E. of regression1.292140    Akaike info

23、 criterion3.351521Sum squared resid1596.162    Schwarz criterion3.356603Log likelihood-1602.703    Hannan-Quinn criter.3.353457Durbin-Watson stat2.020315由上表可知，對常數的回歸結果并不顯著。下面得到殘差平方的自相關圖：Date: 12/16/14 Time: 08:18Sample: 1 957Included observations: 957Autocorre

24、lationPartial CorrelationAC  PAC Q-Stat Prob        | |        | |10.0500.0502.37710.123        |* |        |* |20.1070.

25、10513.3800.001        | |        | |30.0200.01013.7690.003        | |        | |40.0350.02314.9580.005      &#

26、160; | |        | |50.0200.01415.3310.009        | |        | |60.0310.02416.2710.012        |* |      &#

27、160; |* |70.0840.07823.0700.002        | |        | |80.0150.00123.2780.003        | |        | |90.0450.02725.2120.003  

28、0;     | |        | |100.0610.05428.8180.001        | |        | |110.014-0.00328.9990.002        | |  &#

29、160;     | |120.0390.02530.4920.002        | |        | |130.0530.04433.2610.002        | |        | |140.003-0.018

30、33.2680.003        | |        | |15-0.001-0.01433.2690.004        | |        | |16-0.003-0.01133.2780.007      

31、;  | |        | |170.0200.01033.6570.009        | |        | |180.0430.04135.4500.008        | |     

32、0;  | |190.006-0.01035.4900.012        | |        | |200.0320.01436.4860.013        | |        | |210.0540.05239.3340.009 

33、60;      | |        | |22-0.022-0.03939.8290.011        | |        | |230.0140.00140.0120.015        | | 

34、       | |24-0.047-0.04842.2160.012        | |        | |250.0100.00342.3220.017        | |        | |26-

35、0.016-0.00942.5850.021        | |        | |27-0.021-0.03043.0140.026        | |        | |280.0250.02343.6420.030    &#

36、160;   | |        | |29-0.037-0.03144.9790.030        | |        | |300.0290.01945.7970.032        | |    

37、;    | |310.0230.03146.3430.038        | |        | |320.0320.02747.3390.040        | |        | |33-0.038-0.04548.7650.

38、038        | |        | |340.0190.02249.1340.045        | |        | |350.0250.03049.7340.051        

39、;| |        | |360.0160.01849.9840.061圖4.4 殘差平方的自相關圖由上圖可知，殘差平方序列在滯后三階并不異于零，即存在自相關性，進一步進行lm檢驗，這里選取滯后將階數為3，檢驗結果如下：表4.3 ARCH效應檢驗結果Heteroskedasticity Test: ARCHF-statistic4.373176    Prob. F(3,950)0.0046Obs*R-squared12.99530   &#

40、160;Prob. Chi-Square(3)0.0046 由上表可知，p值為0.0046，因此在1%的顯著水平下是存在ARCH效應的。選擇滯后階數更高的進行檢驗,發現滯后4階也滿足在1%的顯著水平下存在ARCH效應，再選取其他高階進行檢驗，發現高階殘差平方項均不滿足。4.3 模型的估計分別估計ARCH（2）、ARCH（1）和GARCH（1，1），由于R不存在自相關性，而且對常數回歸也不顯著，因此不對均值方程進行設定，之設定方差方程。AECH（2）估計結果如下：表4.4 arch（2）模型的估計結果Dependent Variable: RMethod: ML - ARCH (Marquard

41、t) - Normal distributionDate: 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 EquationC1.4

42、099610.07656018.416520.0000RESID(-1)20.0475310.0214202.2190530.0265RESID(-2)20.1062840.0239774.4328490.0000R-squared-0.000066    Mean dependent var0.010480Adjusted R-squared0.000979    S.D. dependent var1.292140S.E. of regression1.291507    

43、;Akaike info criterion3.336256Sum squared resid1596.268    Schwarz criterion3.351503Log likelihood-1593.399    Hannan-Quinn criter.3.342063Durbin-Watson stat2.020182 可以看出，殘差平方滯后項的系數在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）模型的估計結果Dependent Variable: RM

44、ethod: ML - ARCH (Marquardt) - Normal distributionDate: 12/16/14 Time: 08:40Sample: 1 957Included observations: 957Convergence achieved after 7 iterationsPresample variance: backcast (parameter = 0.7)GARCH = C(1) + C(2)*RESID(-1)2VariableCoefficientStd. Errorz-StatisticProb.  Variance Equa

45、tionC1.5948100.06252025.508840.0000RESID(-1)20.0432670.0207012.0901310.0366R-squared-0.000066    Mean dependent var0.010480Adjusted R-squared0.000979    S.D. dependent var1.292140S.E. of regression1.291507    Akaike info criterion3.350173Su

46、m squared resid1596.268    Schwarz criterion3.360337Log likelihood-1601.058    Hannan-Quinn criter.3.354044Durbin-Watson stat2.020182 可以看出，殘差平方滯后項的系數在5%的顯著水平下顯著，因此選擇ARCH（1）合適。下面對GARCH（1，1）進行估計。表4.6 GARCH（1，1）模型的估計結果Dependent Variable: RMethod: ML - ARCH (Marqu

47、ardt) - 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

48、.0463730.0223702.0730260.0382RESID(-1)20.0383960.0091944.1762960.0000GARCH(-1)0.9348960.01941048.165150.0000R-squared-0.000066    Mean dependent var0.010480Adjusted R-squared0.000979    S.D. dependent var1.292140S.E. of regression1.291507   

49、0;Akaike info criterion3.326751Sum squared resid1596.268    Schwarz criterion3.341998Log likelihood-1588.850    Hannan-Quinn criter.3.332558Durbin-Watson stat2.020182 以上模型的系數均滿足非負性，而且在5%的水平下顯著。 4.4模型殘差的檢驗下面進行殘差的自相關性的檢驗，檢驗結果如下：Date: 12/16/14 Time: 08:50Sample:

50、1 957Included observations: 957AutocorrelationPartial CorrelationAC  PAC Q-Stat Prob        | |        | |10.0020.0020.00420.949        | |   

51、60;    | |20.0200.0200.39500.821        | |        | |3-0.006-0.0060.42600.935        | |        | |4-0.011-0.0110.54150

52、.969        | |        | |50.0250.0251.14810.950        | |        | |6-0.050-0.0503.57430.734       

53、0;| |        | |70.0620.0617.29700.399        | |        | |80.0050.0077.32610.502        | |        

54、;| |90.0220.0207.79880.555        | |        | |100.0500.04910.1920.424        | |        | |110.0110.01410.3130.502    

55、    | |        | |12-0.041-0.04811.9260.452        | |        | |13-0.038-0.03113.3050.425        | |   &

56、#160;    | |140.0390.03814.7610.395        | |        | |150.0090.00814.8320.464圖4.5 ARCH(2)模型殘差項的自相關圖Date: 12/16/14 Time: 08:51Sample: 1 957Included observations: 957AutocorrelationPartial Correlatio

57、nAC  PAC Q-Stat Prob        | |        | |1-0.004-0.0040.01900.890        | |        | |20.0320.0321.01080.603 

58、0;      | |        | |3-0.005-0.0051.03510.793        | |        | |4-0.007-0.0091.08870.896        | | &

59、#160;      | |50.0280.0291.86690.867        | |        | |6-0.039-0.0393.34970.764        | |        | |70.066

60、0.0647.56140.373        | |        | |80.0120.0157.70170.463        | |        | |90.0290.0258.50820.484      

61、  | |        | |100.0550.05411.4800.321        | |        | |110.0150.01711.6990.387        | |      

62、;  | |12-0.044-0.05313.6200.326        | |        | |13-0.036-0.03214.8600.316        | |        | |140.0340.03416.0130.313 &

63、#160;      | |        | |150.0050.00516.0400.379圖4.6 ARCH(1)模型殘差項的自相關圖Date: 12/16/14 Time: 08:52Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationAC  PAC Q-Stat Prob   

64、0;    | |        | |10.0100.0100.08940.765        | |        | |20.0360.0361.31900.517        | |    

65、;    | |3-0.001-0.0011.31960.724        | |        | |4-0.000-0.0011.31960.858        | |        | |50.0300.0312.21290.8

66、19        | |        | |6-0.042-0.0423.89170.691        | |        | |70.0600.0597.39280.389        

67、| |        | |80.0050.0067.41370.493        | |        | |90.0270.0228.09450.525        | |        |

68、 |100.0600.05911.6070.312        | |        | |110.0140.01311.7860.380        | |        | |12-0.044-0.05413.6300.325    

69、;    | |        | |13-0.033-0.02814.6930.327        | |        | |140.0380.03816.0880.308        | |   &#

70、160;    | |150.0040.00316.1000.375圖4.7 GARCH(1,1)模型殘差項的自相關圖觀察殘差的自相關圖，可以看出均不存在自相關性。下面觀察殘差平方的自相關圖。Date: 12/16/14 Time: 08:53Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationAC  PAC Q-Stat Prob       

71、0;| |        | |1-0.023-0.0230.52670.468        | |        | |2-0.001-0.0020.52790.768        | |       &

72、#160;| |3-0.002-0.0020.53040.912        | |        | |40.0020.0020.53330.970        | |        | |50.0010.0010.53360.991   &#

73、160;    | |        | |60.0250.0251.11770.981        | |        | |70.0700.0715.88080.554        | |   

74、60;    | |80.0010.0045.88150.660        | |        | |90.0550.0568.85050.451        | |        | |100.0690.07313.4890.19

75、8        | |        | |110.0070.01113.5330.260        | |        | |120.0250.02614.1220.293        |

76、 |        | |130.0300.02914.9920.308        | |        | |140.0070.00415.0390.376        | |        

77、| |15-0.005-0.00715.0620.447圖4.8 ARCH(2)模型殘差平方的自相關圖Date: 12/16/14 Time: 08:54Sample: 1 957Included observations: 957AutocorrelationPartial CorrelationAC  PAC Q-Stat Prob        | |        | |1-0.000-0

78、.0000.00020.990        |* |        |* |20.1090.10911.4110.003        | |        | |30.0010.00111.4130.010      

79、;  | |        | |40.0270.01512.1010.017        | |        | |50.0050.00512.1260.033        | |      

80、  | |60.0280.02312.8620.045        |* |        |* |70.0870.08720.1080.005        | |        | |80.0100.00520.2120.010  &

81、#160;     | |        | |90.0430.02521.9980.009        | |        | |100.0630.06225.9050.004        | |  &

82、#160;     | |110.005-0.00525.9290.007        | |        | |120.0400.02627.4540.007        | |        | |130.0470.04329.6030.005       &