Why doesn't my ARIMA forecast include the trend? Why doesn't my forecast include the upwards drift?  (I can get it to work for AirPassengers, but not for my simulated data.  See graphs below.)  
# simulate time series with drift
set.seed(1234)  
x<-arima.sim(n=365,list(order=c(2,1,0),ar=c(0.7,-0.4)))  
drift<-seq(100,150,length=366)  
x<-x+drift  

# forecast time series
fit<-arima(x,order=c(2,1,0))  
p<-predict(fit,n.ahead=100)$pred  

# plot forecast on the same graph as original data    
layout(2:1)  
plot(x,type="l",xlim=c(0,466),col="blue")  
ptimes<-seq(366,465,by=1)  
lines(ptimes,p,col="red")  

# forecast AirPassengers and plot on the same graph as original data
fit<-arima(AirPassengers,order=c(1,1,0),seasonal=list(order=c(1,1,0)))  
plot(AirPassengers,xlim=c(1949,1963),ylim=c(100,700),col="blue")  
p<-predict(fit,n.ahead=24)$pred  
ptimes<-seq(1961,1962+11/12,by=1/12)  
lines(ptimes,p,col="red")  

My assignment is to use only the in-built packages. I'm sure the forecast package can do this for me but alas ...
(Also, I reckon I should predict a multiplicative trend to AirPassengers.  How could I do that in base R please?)
 A: Look at your model fitting output:
> (fit<-arima(x,order=c(2,1,0))  )

Call:
arima(x = x, order = c(2, 1, 0))

Coefficients:
         ar1      ar2
      0.7659  -0.4139
s.e.  0.0477   0.0477

Your estimated AR(2) coefficients are $(0.76,-0.41)$. This AR(2) process decays to zero quite quickly. So since you have an integrated process of order one, the forecasts are the cumulative sum of this AR(2) process. And since the AR(2) process decays, the increments are pretty much zero immediately, so overall you essentially get a nonzero flat line.
So what you would need would be a nonzero mean for the ARMA process with which you model the differenced seriers. Unfortunately, ?arima tells you that the include.mean parameter is ignored for differenced data.
One way forward would be to use auto.arima() from the forecast package:
plot(forecast(auto.arima(x),h=100))


Alternatively, or if you are limited to R's builtin functions, you could difference the raw data outside arima(), fit and forecast (so include.mean=TRUE would make a difference), and finally calculate cumulative sums yourself.
