1、所使用的程序:
myspec=ugarchspec(variance.model = list(model="sGARCH",garchOrder=c(1,1),submodel=NULL,
external.regressors=NULL,variance.targeting=FALSE),
mean.model =list(armaOrder=c(2,1),include.mean=TRUE,archm=TRUE,archpow=1,
arfima=FALSE,external.regressors=NULL,archex=FALSE),
distribution.model = "sstd" )
myfit=ugarchfit(myspec,data=sensex,out.sample = 0,solver = "solnp")
myfit
2、结果展示:
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : sGARCH(1,1)
Mean Model : ARFIMA(2,0,1)
Distribution : sstd
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu 0.002763 0.000286 9.6509 0.000000
ar1 1.013878 0.001816 558.3100 0.000000
ar2 -0.050961 0.004946 -10.3034 0.000000
ma1 -0.996567 0.000108 -9255.8790 0.000000
archm -0.244336 0.027494 -8.8870 0.000000
omega 0.000005 0.000000 10.7874 0.000000
alpha1 0.095744 0.028119 3.4050 0.000662
beta1 0.847541 0.019656 43.1196 0.000000
skew 1.035303 0.053529 19.3411 0.000000
shape 5.731527 1.090814 5.2544 0.000000
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.002763 0.000295 9.3693 0.000000
ar1 1.013878 0.002014 503.3106 0.000000
ar2 -0.050961 0.005819 -8.7580 0.000000
ma1 -0.996567 0.000146 -6827.1368 0.000000
archm -0.244336 0.035157 -6.9499 0.000000
omega 0.000005 0.000001 8.2793 0.000000
alpha1 0.095744 0.027748 3.4505 0.000559
beta1 0.847541 0.021056 40.2523 0.000000
skew 1.035303 0.051871 19.9592 0.000000
shape 5.731527 1.012597 5.6602 0.000000
LogLikelihood : 2452.114
Information Criteria
------------------------------------
Akaike -6.6724
Bayes -6.6097
Shibata -6.6728
Hannan-Quinn -6.6482
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.04345 0.8349
Lag[2*(p+q)+(p+q)-1][8] 1.93689 1.0000
Lag[4*(p+q)+(p+q)-1][14] 3.18409 0.9953
d.o.f=3
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.432 0.5110
Lag[2*(p+q)+(p+q)-1][5] 2.119 0.5906
Lag[4*(p+q)+(p+q)-1][9] 4.574 0.4945
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.004977 0.500 2.000 0.9438
ARCH Lag[5] 0.619187 1.440 1.667 0.8480
ARCH Lag[7] 1.688856 2.315 1.543 0.7828
Nyblom stability test
------------------------------------
Joint Statistic: 37.0777
Individual Statistics:
mu 0.09976
ar1 0.05244
ar2 0.05349
ma1 0.06245
archm 0.11016
omega 5.03191
alpha1 0.14839
beta1 0.22968
skew 0.08607
shape 0.03572
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 2.29 2.54 3.05
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.8997 0.368601
Negative Sign Bias 1.2806 0.200735
Positive Sign Bias 2.5969 0.009596 ***
Joint Effect 10.7271 0.013297 **
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 21.44 0.3129
2 30 33.25 0.2679
3 40 47.45 0.1660
4 50 45.46 0.6175
Elapsed time : 1.069057
3、是否可理解为均值方程中条件标准差?
GARCH-M模型