m1=arima(da1,order=c(1,1,0),seasonal=list(order=c(2,1,0),period=12),method="ML")
m2=arima(da1,order=c(1,1,1))
m3=arima(da1,order=c(2,1,0))
m4=arima(da1,order=c(0,1,3))
m5 <- auto.arima(da1)
yichang.m1=arimax(x = da1, order = c(1, 1, 0), seasonal = list(order = c(2, 1, 0), period = 12), xtransf=data.frame(I0910=1*(seq(da1)==35),I0910=1*(seq(da1)==47)),transfer=list(c(0,0),c(1,0)) )
Series: da1
ARIMA(1,1,0)(2,1,0)[12]
Coefficients:
ar1 sar1 sar2 I0910-MA0 I0910.1-AR1 I0910.1-MA0
0.7790 -0.9910 -0.6312 -0.6259 1.0074 1.4177
s.e. 0.0692 0.0834 0.0799 0.3031 0.0412 0.4357
sigma^2 estimated as 0.4434: log likelihood=-93.3
AIC=198.6 AICc=200.09 BIC=215.53
yichang.m2=arimax(da1,order=c(1,1,1),xtransf=data.frame(I0910=1*(seq(da1)==35),I0910=1*(se q(da1)==47)),transfer=list(c(0,0),c(1,0)))
Series: da1
ARIMA(1,1,1)
Coefficients:
ar1 ma1 I0910-MA0 I0910.1-AR1 I0910.1-MA0
0.6804 0.4223 -0.6655 0.9989 1.1897
s.e. 0.0848 0.0957 0.2065 0.0543 0.3833
sigma^2 estimated as 0.3583: log likelihood=-86.71
AIC=183.41 AICc=184.37 BIC=198.74
yichang.m3=arimax(da1,order=c(2,1,0),xtransf=data.frame(I0910=1*(seq(da1)==35),I0910=1*(se q(da1)==47)),transfer=list(c(0,0),c(1,0)))
Series: da1
ARIMA(2,1,0)
Coefficients:
ar1 ar2 I0910-MA0 I0910.1-AR1 I0910.1-MA0
1.0891 -0.3466 -0.6544 1.0082 1.1721
s.e. 0.0963 0.0959 0.2190 0.0326 0.3997
sigma^2 estimated as 0.3613: log likelihood=-87.11
AIC=184.21 AICc=185.17 BIC=199.53
yichang.m4=arimax(da1,order=c(0,1,3),xtransf=data.frame(I0910=1*(seq(da1)==35),I0910=1*(se q(da1)==47)),transfer=list(c(0,0),c(1,0)))
Series: da1
ARIMA(0,1,3)
Coefficients:
ma1 ma2 ma3 I0910-MA0 I0910.1-AR1 I0910.1-MA0
1.0846 0.6137 0.1333 -0.5280 1.0059 1.2618
s.e. 0.1003 0.1221 0.0860 0.2122 0.0259 0.3893
sigma^2 estimated as 0.3719: log likelihood=-88.43
AIC=188.86 AICc=190.15 BIC=206.74
yichang.m5=arimax(da1,order=c(2,1,1),xtransf=data.frame(I0910=1*(seq(da1)==35),I0910=1*(se q(da1)==47)),transfer=list(c(0,0),c(1,0)))
Series: da1
ARIMA(2,1,1)
Coefficients:
ar1 ar2 ma1 I0910-MA0 I0910.1-AR1 I0910.1-MA0
0.8663 -0.1711 0.2566 -0.6526 1.0001 1.1686
s.e. 0.2369 0.2038 0.2350 0.2070 0.0493 0.3817
sigma^2 estimated as 0.3567: log likelihood=-86.5
AIC=185.01 AICc=186.29 BIC=202.88
Box-Ljung test
Box.test(resm1,lag=5,type="Ljung")
Box-Ljung test
data: resm1
X-squared = 10.9613, df = 5, p-value = 0.05215
> Box.test(resm2,lag=5,type="Ljung")
Box-Ljung test
data: resm2
X-squared = 3.1873, df = 5, p-value = 0.6711
> Box.test(resm3,lag=5,type="Ljung")
Box-Ljung test
data: resm3
X-squared = 5.3676, df = 5, p-value = 0.3727
> Box.test(resm4,lag=5,type="Ljung")
Box-Ljung test
data: resm4
X-squared = 7.6986, df = 5, p-value = 0.1736 Box.test(resm5,lag=5,type="Ljung")
Box-Ljung test
data: resm5
X-squared = 3.3973, df = 5, p-value = 0.639 P值均大于0.05，即模型通过
再进行异常值检验结果如下：
McLeod.Li.test(y=resm1)
McLeod.Li.test(y=resm2)
McLeod.Li.test(y=resm3)
McLeod.Li.test(y=resm4)
McLeod.Li.test(y=resm5)
pacf(resm2^2,lag=60)
Garch（0,1）模型
Garchm2= garch(resm2,order=c(0,1),cond.dist="std",trace=F)
summary(Garchm2)
模型系数不显著，即异方差不通过
m4 <- garchFit(formula = ~arma(1,1)+garch(1,0),data=da3,cond.dist="std") ### arma(1,1)+arch(1)。