时间序列作业.docx

时间序列作业.docx

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时间序列作业（P188第六题）

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5-19（行数据）所示表5-19

4.99

5

5.03

5.03

5.25

5.26

5.3

5.45

5.49

5.68

5.65

5.8

6.5

6.45

6.48

6.45

6.35

6.4

6.44

6.45

6.48

6.4

6.35

6.4

6.3

6.32

6.35

5.58

5.18

5.18

5.17

5.15

5.21

5.23

5.05

4.65

4.67

4.69

4.68

4.62

4.63

4.9

5.44

5.56

6.04

8.07

8.07

8.1

8.05

8.06

8.07

8.06

8.11

8.6

11

11

9.48

9.18

8.62

8.3

8.47

8.44

8.44

8.54

8.54

8.5

8.44

8.49

8.4

8.46

8.5

8.5

8.47

8.48

8.48

8.54

8.56

8.39

8.89

9.91

9.89

9.9

9.88

9.86

9.86

9.74

9.42

9.27

9.26

8.99

8.83

8.82

8.83

8.83

8.79

8.79

8.69

8.66

8.67

9

9.61

9.7

9.94

9.94

9.94

9.95

9.94

9.96

10.75

11.2

11.4

11.54

11.5

11.34

11.5

11.5

11.58

13.1

13.12

13.1

13.15

13.1

13.2

14.2

14.75

14.6

14.5

14.8

15.85

16.2

16.5

16.4

16.4

16.35

16.1

14

12.3

12

14.35

14.6

12.5

12.75

13.7

13.45

12

11

11.6

12.05

12.35

12.7

12.45

12.55

12.2

11.85

12.1

12.5

12.9

12.5

13.2

13.65

13.65

13.5

14.45

14.3

15.05

15.55

15.65

14.65

14.15

13.3

12.65

14.5

15.1

15.15

14.3

14.25

14.05

14.7

15.05

14.05

13

12.85

12.6

11.8

13

12.35

11.45

11.35

11.55

12.3

11.7

12.05

12.3

12.9

13.05

13.3

13.85

14.65

14.85

15.7

15.4

15.1

14.8

15.8

15.8

15

14.4

14.15

14.45

14.1

14.05

13.75

13.3

13

12.55

12.25

11.1

11.15

10.7

10.25

10.55

10.25

10.3

9.6

8.4

8.35

8.25

8.3

7.4

7.15

6.35

5.65

7.4

7.2

6.85

6.5

6.25

5.95

5.65

5.85

5.45

5.3

5.2

5.4

5.35

5.1

5.8

6.35

6.5

6.95

8.05

7.85

（1） 考察序列的方差齐性

（2） 选择适当的模型拟合该序列的发展

程序如下：

w=read.table（”习题5.6数据.txt"）

x=w$V2

r.x=diff（log（x））*100

a=arima（r.x,order=c（3,0,3））

par（mfrow=c（2,2））

ts.plot（x）

ts.plot（log（x））

ts.plot（r.x）

ts.plot（residuals（a）,ylab="Residuals"）

y=residuals（a）

plot（density（y）,lty=1,lwd=2）

x=rnorm（length（y））

curve（dnorm（x）,col="green”,lty=2,lwd=2,add=TRUE）library（TSA）

McLeod.Li.test（y）

屁RGraphics:

Device2（ACTIVE）

屁RGraphics:

Device2（ACTIVE）

density.default（x=y）

08.0ooo

点我设置

>library（fGarch）

Loadingrequiredpackage:

timeDate

Loadingrequiredpackage:

timeSeries

Loadingrequiredpackage:

fBasics

RmetricsPackagefBasics

AnalysingMarketsandcalculatingBasicStatistics

Copyright（C）2005-2014RmetricsAssociationZurich

EducationalSoftwareforFinancialEngineeringandComputationalScienceRmetricsisfreesoftwareandcomeswithABSOLUTEYNOWARRANTYhttps:

//www.rmetrics.org---Mailto:

info@rmetrics.org

Warningmessages:

1:

package‘fGarch’wasbuiltunderRversion3.1.2

2:

package‘timeDate’wasbuiltunderRversion3.1.2

3:

package‘timeSeries’wasbuiltunderRversion3.1.2

>a4=garchFit（~arma（1,0）+garch（1,1）,r.x）

SeriesInitialization:

ARMAModel:

arma

FormulaMean:

~arma（1,0）

GARCHModel:

garch

FormulaVariance:

~garch（1,1）

ARMAOrder:

10

MaxARMAOrder:

1

GARCHOrder:

11

MaxGARCHOrder:

1

MaximumOrder:

1

ConditionalDist:

norm

h.start:

2

llh.start:

1

LengthofSeries:

27

RecursionInit:

mci

SeriesScale:

ParameterInitialization:

20.7458

InitialParameters:

$params

LimitsofTransformations:

$U,$V

WhichParametersareFixed?

$includesParameterMatrix:

U

V paramsincludes

mu -0.12078958

0.12078960.007939075

TRUE

ar1 -0.99999999

1.00000000.234298886

TRUE

omega0.00000100100.00000000.100000000

TRUE

alpha10.00000001

1.00000000.100000000

TRUE

gamma1-0.99999999

1.00000000.100000000

FALSE

beta10.00000001

1.00000000.800000000

TRUE

delta0.00000000

2.00000002.000000000

FALSE

skew0.10000000

10.00000001.000000000

FALSE

shape1.00000000

10.00000004.000000000

FALSE

IndexListofParameterstobeOptimized:

muar1

omegaalpha1

beta1

1 2

3 4

6

Persistence:

0.9

---STARTOFTRACE--SelectedAlgorithm:

nlminb

RcodednlminbSolver:

0:

37.574412:

0.007939080.2342990.1000000.1000000.800000

1:

37.128348:

0.007948990.1671880.3333041.00000e-08 0.695922

2:

36.902954:

0.007948610.1746640.3054721.00000e-08 0.664218

3:

36.856091:

0.007946040.2165160.2989431.00000e-08 0.657780

4:

36.850350:

0.007945210.2209960.3066901.00000e-08 0.664983

5:

36.845754:

0.007936390.2267370.3092381.00000e-08 0.655392

6:

36.843474:

0.007889130.2397780.3234891.00000e-08 0.643582

7:

36.842988:

0.007766770.2402370.3307351.00000e-08 0.633896

8:

36.842682:

0.007610320.2404550.3434571.00000e-08 0.619815

9:

36.839712:

0.005232250.2433040.5533641.00000e-08 0.391087

10:

36.839252:

0.004445610.2402410.6050221.00000e-08 0.334519

11:

36.838980:

0.003639310.2388140.6448941.00000e-08 0.290676

12:

36.838327:

0.001480850.2370010.7337141.00000e-08 0.192581

13:

36.836416:

-0.004024660.2348570.9065711.00000e-081.00000e-08

14:

36.834786:

-0.006439440.2355890.9038721.00000e-081.00000e-08

15:

36.830950:

-0.01885830.2407730.8903821.00000e-08 1.00000e-08

16:

36.830919:

-0.01856110.2411920.8910001.00000e-08 1.00000e-08

17:

36.830860:

-0.01842260.2421300.8921111.00000e-08 1.00000e-08

18:

36.830795:

-0.01866460.2427270.8931821.00000e-08 1.00000e-08

19:

36.830668:

-0.01969790.2431420.8951621.00000e-08 1.00000e-08

20:

36.830575:

-0.02102430.2425930.8964351.00000e-08 1.00000e-08

21:

36.830543:

-0.02180660.2416840.8965071.00000e-08 1.00000e-08

22:

36.830540:

-0.02188850.2413310.8962101.00000e-08 1.00000e-08

23:

36.830540:

-0.02185780.2412930.8961201.00000e-08 1.00000e-08

24:

36.830540:

-0.02185200.2412950.8961131.00000e-08 1.00000e-08

FinalEstimateoftheNegativeLLH:

LLH:

118.7038normLLH:

4.396438

mu ar1 omegaalpha1 beta1

-0.45333703 0.24129492385.67626085 0.00000001 0.00000001

beta1

R-optimhessDifferenceApproximatedHessianMatrix:

mu ar1 omegaalpha1

mu-6.741405e-02-6.802707e-02-9.871808e-10-0.11938093-3.297415e-07ar1-6.802707e-02-2.803564e+01-2.267559e-08-30.35044019-7.739587e-06omega-9.871808e-10-2.267559e-08-9.075930e-05-0.01226946-3.370707e-02alpha1-1.193809e-01-3.035044e+01-1.226946e-02-25.849479556.352009e+00beta1-3.297415e-07-7.739587e-06-3.370707e-02 6.35200878-1.250003e+01

attr（,"time"）

Timedifferenceof0.01200104secs

---ENDOFTRACE---

TimetoEstimateParameters:

Timedifferenceof0.04300213secs

>summary（a4）

Title:

GARCHModelling

Call:

garchFit（formula=~arma（1,0）+garch（1,1）,data=r.x）

MeanandVarianceEquation:

data~arma（1,0）+garch（1,1）

0x05b32850>

[data=r.x]

ConditionalDistribution:

norm

Coefficient（s）:

mu ar1 omegaalpha1 beta1

-4.5334e-01 2.4129e-01 3.8568e+02 1.0000e-08 1.0000e-08

Std.Errors:

basedonHessian

ErrorAnalysis:

Std.ErrortvaluePr（>|t|）

Estimate

mu

-4.533e-01

3.856e+00

-0.1180.906416

ar1

2.413e-01

1.896e-01

1.2730.203075

omega

3.857e+02

1.091e+02

3.5360.000406***

alpha1

1.000e-08

1.245e-02

0.0000.999999

beta1

1.000e-08

2.705e-01

0.0001.000000

Signif.codes:

0‘***’0.001‘**’0.01‘*’0.05‘.’0.1‘’1

LogLikelihood:

-118.7038normalized:

-4.396438

Description:

MonFeb0410:

51:

452013byuser:

Administrator

StandardisedResidualsTests:

Statisticp-Value

Jarque-BeraTest

R

ChiA2

2.60177

0.2722907

Shapiro-WilkTest

R

W

0.94326970.1466993

Ljung-BoxTest

R

Q（10）

9.262967

0.5073422

Ljung-BoxTest

R

Q（15）

15.35413

0.4262225

Ljung-BoxTest

R

Q（20）

25.37351

0.1875132

Ljung-BoxTest

RA2

Q（10）

5.081702

0.8856538

Ljung-BoxTest

RA2

Q（15）

7.034229

0.9566929

Ljung-BoxTest

RA2

Q（20）

12.08665

0.9130612

LMArchTest

R

TRA2

13.748190.3170765

InformationCriterionStatistics:

AICBICSICHQIC

9.1632469.4032159.1079569.234601

原序列方差非齐，差分序列方差非齐，对数变换后，差分序列方差齐性