I had some problems fitting an ARIMA - the data are

FTSE <-log(EuStockMarkets[,"FTSE"]) 

The following link explains the problem and gives the solution http://www.stat.pitt.edu/stoffer/tsa3/Rissues.htm#Issue2
The solution sounded effective, untill I tried some $ARIMA(p,d,q)$ other than $ARIMA(1,1,0)$: with $ARIMA(1,1,1)$, $ARIMA(2,1,1)$ and $ARIMA(1,1,2)$ the procedure (1+) and the procedure (2) give different coefficients, in particular with the procedure (1+) it says that the AR part is not stationary (indeed changing method from 'css' to 'ml' the coeffiecient of $AR$ is 1 or above).
These are the codes for $ARIMA(1,1,1)$:

model2<-Arima(dFTSE, order = c(1, 0, 1))
model1pluscss<-Arima(FTSE,order=c(1,1,1), xreg=1:length(FTSE))
model1plusml<-Arima(FTSE,order=c(1,1,1), xreg=1:length(FTSE), method='ML')

On the other side the two procedures produce the same output also in $ARIMA(0,1,1)$ and $ARIMA(0,1,2)$. Is there a theoretical explanation that I can't see or something else?


The problem is with the arima() function, not the Arima() function from the forecast package. The Arima() function has an argument include.drift which is TRUE by default when $d>1$.

So your models model1pluscss and model1plusml try to include a drift term twice, and so produce some numerical problems that are manifest in different ways.

The model you want is simply

model1 <- Arima(FTSE, order=c(1,1,1))

That is not identical to your model2 because ARIMA models in R are estimated using a state space representation and the non-​​stationary components are given a diffuse prior, rather than simply differenced away. (See help(arima) in R.) This will lead to different parameter estimates.


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