library(forecast)
data<-c(1,4,3,5,7,8,1,2,6,7,2,3,4,4);
mymodel<-Arima(data[1:10], order=c(1,1,1)) # Fitting the model using data from 1 to 10

forecast(mymodel, h=1)$mean[1] # Forecasting point 11
[1] 5.263669

fitted(Arima(data[1:11],  model = mymodel))[11] # Applying the model estimated from 1 to 10 to data from 1 to 11 and taking fitted values
[1] 5.125379

> mymodel
Series: data[1:10]
ARIMA(1,1,1)

Coefficients:
         ar1      ma1
      0.3417  -0.9999
s.e.  0.4143   0.7224

mymodel <- Arima(data[1:10], order=c(1,0,1))
forecast(mymodel, h=1)$mean[1] # Forecasting point 11
# 4.98265
mymodel2 <- Arima(data[1:11],  model = mymodel)
fitted(mymodel2)[11]
# 4.98265