广义异方差模型例题

广义异方差模型例题：例：1969年1月至1994年9月澳大利亚储备银行2年期有价证券月度利率数据如表所示（行数据）4.99

5

5.03

5.03

5.25

5.26

5.3

5.45

5.49

5.52

5.7

5.68

5.65

5.8

6.5

6.45

6.48

6.45

6.35

6.4

6.43

6.43

6.44

6.45

6.48

6.4

6.35

6.4

6.3

6.32

6.35

6.13

5.7

5.58

5.18

5.18

5.17

5.15

5.21

5.23

5.05

4.65

4.65

4.6

4.67

4.69

4.68

4.62

4.63

4.9

5.44

5.56

6.04

6.06

6.06

8.07

8.07

8.1

8.05

8.06

8.07

8.06

8.11

8.6

10.8

11

11

11

9.48

9.18

8.62

8.3

8.47

8.44

8.44

8.46

8.49

8.54

8.54

8.5

8.44

8.49

8.4

8.46

8.5

8.5

8.47

8.47

8.47

8.48

8.48

8.54

8.56

8.39

8.89

9.91

9.89

9.91

9.91

9.9

9.88

9.86

9.86

9.74

9.42

9.27

9.26

8.99

8.83

8.83

8.83

8.82

8.83

8.83

8.79

8.79

8.69

8.66

8.67

8.72

8.77

9

9.61

9.7

9.94

9.94

9.94

9.95

9.94

9.96

9.97

10.83

10.75

11.2

11.4

11.54

11.5

11.34

11.5

11.5

11.58

12.42

12.85

13.1

13.12

13.1

13.15

13.1

13.2

14.2

14.75

14.6

14.6

14.45

14.5

14.8

15.85

16.2

16.5

16.4

16.4

16.35

16.1

13.7

13.5

14

12.3

12

14.35

14.6

12.5

12.75

13.7

13.45

13.55

12.6

12

11

11.6

12.05

12.35

12.7

12.45

12.55

12.2

12.1

11.15

11.85

12.1

12.5

12.9

12.5

13.2

13.65

13.65

13.5

13.45

13.35

14.45

14.3

15.05

15.55

15.65

14.65

14.15

13.3

12.65

12.7

12.8

14.5

15.1

15.15

14.3

14.25

14.05

14.7

15.05

14.05

13.8

13.25

13

12.85

12.6

11.8

13

12.35

11.45

11.35

11.55

10.85

10.9

12.3

11.7

12.05

12.3

12.9

13.05

13.3

13.85

14.65

15.05

15.15

14.85

15.7

15.4

15.1

14.8

15.8

15.8

15

14.4

13.8

14.3

14.15

14.45

14.1

14.05

13.75

13.3

13

12.55

12.25

11.85

11.5

11.1

11.15

10.7

10.25

10.55

10.25

10.3

9.6

8.4

8.2

7.25

8.35

8.25

8.3

7.4

7.15

6.35

5.65

7.4

7.2

7.05

7.1

6.85

6.5

6.25

5.95

5.65

5.85

5.45

5.3

5.2

5.55

5.15

5.4

5.35

5.1

5.8

6.35

6.5

6.95

8.05

7.85

7.75

8.6

（1）考察该序列的方差齐性。（2）选择适当的模型拟合该序列的发展解答：（1）1、时序图：时序图显示序列存在曲线趋势，我们对原序列进行差分得到残差序列的图。差分后的残差图整均值平稳，但伴随大小不等的随机波动。我们对残差序列进行自回归，再考察自回归残差序列的方差齐性。2、用AUTOREG过程建立序列｛Xt｝关于一阶滞后项lagx的回归模型，并检验残差序列的自相关性和异方差性。检验显示Dh统计量为1.8550,Dh统计量的P值为0.0318小于0.05,结果显示残差序列具有显著的自相关性。显示回归模型常数截距项不显著（0.0736>0.05）。显示残差序列具有显著的异方差性。3、arch的定阶procautoregdata=hh;modelx=lagx/lagdep=lagxarchtest;modelx=lagx/nlag=4backstepgarch=(p=1,q=1);outputout=rescev=v;run;参数检验显示除AR5参数不显著外，其它参数显著。综合考虑残差序列自相关性和异方差性检验结果，尝试拟合无回归常数项的广义异方差模型，nlag=4，garch=(p=1,q=1)。4、异方差模型：拟合效果很理想。（其中e^t~n(0,0.26999)）附程序：datahh;inputx@@;difx=dif(x);lagx=lag(x);year=intnx("month","01jan1969"d,_n_-1);formatyearmonyy7.;cards;4.9955.035.035.255.265.35.455.495.525.75.685.655.86.56.456.486.456.356.46.436.436.446.456.486.46.356.46.36.326.356.135.75.585.185.185.175.155.215.235.054.654.654.64.674.694.684.624.634.95.445.566.046.066.068.078.078.18.058.068.078.068.118.610.81111119.489.188.628.38.478.448.448.468.498.548.548.58.448.498.48.468.58.58.478.478.478.488.488.548.568.398.899.919.899.919.919.99.889.869.869.749.429.279.268.998.838.838.838.828.838.838.798.798.698.668.678.728.7799.619.79.949.949.949.959.949.969.9710.8310.7511.211.411.5411.511.3411.511.511.5812.4212.8513.113.1213.113.1513.113.214.214.7514.614.614.4514.514.815.8516.216.516.416.416.3516.113.713.51412.31214.3514.612.512.7513.713.4513.5512.6121111.612.0512.3512.712.4512.5512.212.111.1511.8512.112.512.912.513.213.6513.6513.513.4513.3514.4514.315.0515.5515.6514.6514.1513.312.6512.712.814.515.115.1514.314.2514.0514.715.0514.0513.813.251312.8512.611.81312.3511.4511.3511.5510.8510.912.311.712.0512.312.913.0513.313.8514.6515.0515.1514.8515.715.415.114.815.815.81514.413.814.314.1514.4514.114.0513.7513.31312.5512.2511.8511.511.111.1510.710.2510.5510.2510.39.68.48.27.258.358.258.37.47.156.355.657.47.27.057.16.856.56.255.955.655.855.455.35.25.555.155.45.355.15.86.356.56.958.057.857.758.6;run;procgplotdata=hh;plot(xdifx)*year;symboli=line;run;procautoregdata=hh;modelx=lagx/lagdep=lagxarchtest;modelx=lagx/nlag=4backstepgarch=(p=1,q=1)noint;outputout=outp=ppm=pmr=rrm=rmucl=ucllcl=lclcev=cev;run;dataout;setout;uclr=1.96*sqrt(0.26747);lclr=-1.96*sqrt(0.26747);cuclr=1.96*sqrt(cev);clclr=-1.96*sqrt(cev);cuclp=p+1.96*sqrt(cev);clclp=p-1.96*sqrt(cev);run;procgplotdata=out;plotx*year=1p*year=2cuclp*year=3clclp*year=3lcl*year=4ucl*year=4/overlay;symbol1c=blacki=nonev=star;symbol2c=redi=linev=none;symbol3c=bluei=lnie;symbol4c=greeni=joinv=star