为什么auto.arima()和Arima()不同？

Question

我用函数auto.arima()拟合模型，然后尝试用相同的模型重新拟合函数Arima()，但是得到了不同的结果。

由auto.arima()

> a<-c(90,88,96,110,105,128,119,117,155,135,138,127,156,168,145,160,180,175,189,166,184)
> chuoi<-ts(a,frequency=1,start=c(1990))
> auto.arima(chuoi)
Series: chuoi 
ARIMA(2,1,0) with drift         

Coefficients:
          ar1      ar2   drift
      -0.7075  -0.4648  4.7897
s.e.   0.1930   0.1972  1.3689

sigma^2 estimated as 163.1:  log likelihood=-79.7
AIC=167.39   AICc=170.06   BIC=171.38

通过Arima()使用相同的模型，使用了所有方法“CSS”、"ML“和"CSS"：

> fit210<-Arima(chuoi,c(2,1,0),method="ML")
> fit210
Series: chuoi 
ARIMA(2,1,0)                    

Coefficients:
          ar1      ar2
      -0.4670  -0.1928
s.e.   0.2162   0.2201

sigma^2 estimated as 244.2:  log likelihood=-83.48
AIC=172.96   AICc=174.46   BIC=175.95
> fit210<-Arima(chuoi,c(2,1,0),method="CSS")
> fit210
Series: chuoi 
ARIMA(2,1,0)                    

Coefficients:
          ar1      ar2
      -0.4876  -0.2111
s.e.   0.2196   0.2304

sigma^2 estimated as 268.3:  part log likelihood=-84.3
> fit210<-Arima(chuoi,c(2,1,0),method="CSS-ML")
> fit210
Series: chuoi 
ARIMA(2,1,0)                    

Coefficients:
          ar1      ar2
      -0.4671  -0.1928
s.e.   0.2162   0.2201

sigma^2 estimated as 244.2:  log likelihood=-83.48
AIC=172.96   AICc=174.46   BIC=175.95

很明显，我得到了不同的系数ar(1)，ar(2)。那么，函数auto.arima()如何计算系数ar(1)，ar(2)？

Answer 1

你的第一个模型包括漂移，你需要运行它

Arima(chuoi,c(2,1,0),include.drift = TRUE)

这两者是相同的：

auto.arima(chuoi) 
Arima(chuoi,c(2,1,0),include.drift = TRUE) # default model, but with drift

输出：

> auto.arima(chuoi)
Series: chuoi 
ARIMA(2,1,0) with drift         

Coefficients:
          ar1      ar2   drift
      -0.7075  -0.4648  4.7897
s.e.   0.1930   0.1972  1.3689

sigma^2 estimated as 163.1:  log likelihood=-79.7
AIC=167.39   AICc=170.06   BIC=171.38



>   Arima(chuoi,c(2,1,0),include.drift = T)
Series: chuoi 
ARIMA(2,1,0) with drift         

Coefficients:
          ar1      ar2   drift
      -0.7075  -0.4648  4.7897
s.e.   0.1930   0.1972  1.3689

sigma^2 estimated as 163.1:  log likelihood=-79.7
AIC=167.39   AICc=170.06   BIC=171.38
>