![](https://bbs-cdn.datacourse.cn/static/image/filetype/rar.gif)
sp500=read.table("sp500.txt")
sp500.returns=diff(log(sp500$V1))*100
auto.arima(sp500.returns) #要加载forecast包
m1=auto.arima(sp500.returns)
res1=residuals(m1)
Box.test(res1) #为白噪声
ArchTest(res1) #要加载FinTS包 有异方差
ArchTest(res1^2) #居然没有了异方差,很奇怪
以下用GARCH(1,1)-M模型拟合,要用到rugarch包
variance.model=list(model="fGARCH",garchOrder=c(1,1), submodel="GARCH") #方差模型
mean.model=list(armaOrder=c(0,2),include.mean=TRUE,garchInMean=TRUE,inMeanType=2,arfima=FALSE) #均值模型
spec=ugarchspec(variance.model=variance.model,mean.model=mean.model, distribution.model="std") #两个模型结合
fit=ugarchfit(data=sp500.returns,spec=spec,out.sample=0,solver="solnp")
fit
这段GARCH(1,1)-M模型拟合的返回结果放在了doc文件中
以下单独对fit残差
ArchTest(residuals(fit))
McLeod.Li.test(residuals(fit)) #要加载TSA包
都显示有方差异性,我认为和doc文件中的红色加深部分矛盾
ArchTest(residuals(fit)^2)
McLeod.Li.test(y=residuals(fit)^2) #奇了怪了,残差平方后,就方差齐性了
McLeod.Li.test(y=residuals(fit)^2.1) #但这又方差异性了
Box.test(residuals(fit)) #原来ma2模型残差已是白噪声,但ma2+GARCH(1,1)-M 模型的残差反而不是白噪声了,很奇怪
GARCH(1,1)-M模型拟合返回结果
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : fGARCH(1,1)
fGARCH Sub-Model : GARCH
Mean Model : ARFIMA(0,0,2)
Distribution : std
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu 0.054826 0.005660 9.6858 0.0e+00
ma1 0.098061 0.008087 12.1255 0.0e+00
ma2 -0.028445 0.007261 -3.9177 8.9e-05
omega 0.005980 0.000932 6.4160 0.0e+00
alpha1 0.075629 0.005047 14.9856 0.0e+00
beta1 0.919790 0.005039 182.5500 0.0e+00
shape 6.834882 0.354538 19.2783 0.0e+00
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.054826 0.005960 9.1991 0e+00
ma1 0.098061 0.009211 10.6464 0e+00
ma2 -0.028445 0.006324 -4.4981 7e-06
omega 0.005980 0.001138 5.2542 0e+00
alpha1 0.075629 0.006830 11.0737 0e+00
beta1 0.919790 0.006785 135.5722 0e+00
shape 6.834882 0.437600 15.6190 0e+00
LogLikelihood : -18376.05
Information Criteria
------------------------------------
Akaike 2.3434
Bayes 2.3468
Shibata 2.3434
Hannan-Quinn 2.3446
Q-Statistics on Standardized Residuals
------------------------------------
statistic p-value
Lag10 17.79 0.02289
Lag15 22.12 0.05351
Lag20 27.49 0.07017
H0 : No serial correlation
Q-Statistics on Standardized SquaredResiduals
------------------------------------1
statistic p-value
Lag10 17.53 0.02502
Lag15 20.28 0.08847
Lag20 24.12 0.15100
ARCH LM Tests
------------------------------------
StatisticDoF P-Value
ARCH Lag[2] 12.80 2 0.001666
ARCH Lag[5] 12.97 5 0.023657
ARCH Lag[10] 17.31 10 0.067792
Nyblom stability test
------------------------------------
Joint Statistic: 22.4136
Individual Statistics:
mu 0.2276
ma1 16.6716
ma2 0.6400
omega 2.0735
alpha1 1.9789
beta1 2.6989
shape 1.4570
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.69 1.9 2.35
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.5886 5.561e-01
Negative Sign Bias 4.0662 4.802e-05 ***
Positive Sign Bias 2.5898 9.611e-03 ***
Joint Effect 48.4371 1.719e-10 ***
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 65.28 5.493e-07
2 30 88.29 6.657e-08
3 40 85.56 2.458e-05
4 50 113.59 4.827e-07
Elapsed time : 10.82462
望各位高手赐教,谢谢!