程序如下，数据和doc文件在附件中

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

------------------------------------

EstimateStd. Errort value Pr(>|t|)

mu 0.054826 0.005660 9.6858 0.0e+00

ma1 0.098061 0.00808712.1255 0.0e+00

ma2 -0.028445 0.007261-3.9177 8.9e-05

omega0.005980 0.000932 6.4160 0.0e+00

alpha1 0.075629 0.00504714.9856 0.0e+00

beta10.919790 0.005039 182.55000.0e+00

shape6.834882 0.35453819.2783 0.0e+00

Robust Standard Errors:

EstimateStd. Errort value Pr(>|t|)

mu 0.054826 0.0059609.1991 0e+00

ma1 0.098061 0.00921110.6464 0e+00

ma2 -0.028445 0.006324-4.4981 7e-06

omega 0.005980 0.001138 5.2542 0e+00

alpha10.075629 0.00683011.0737 0e+00

beta1 0.919790 0.006785 135.5722 0e+00

shape 6.834882 0.43760015.6190 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

------------------------------------

StatisticDoFP-Value

ARCH Lag[2] 12.80 2 0.001666

ARCH Lag[5] 12.975 0.023657

ARCH Lag[10] 17.3110 0.067792

Nyblom stability test

------------------------------------

Joint Statistic:22.4136

Individual Statistics:

mu 0.2276

ma1 16.6716

ma2 0.6400

omega2.0735

alpha1 1.9789

beta12.6989

shape1.4570

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 Bias4.0662 4.802e-05 ***

Positive Sign Bias2.5898 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！