Solved – Simulation of ARIMA (1,1,0) series

arimartime series

I have fitted the ARIMA models to the original time series, and the best model is ARIMA(1,1,0). Now I want to simulate the series from that model. I wrote the simple AR(1) model, but I couldn't understand how to adjust the difference within the model ARI(1,1,0).
The following R code for AR(1) series is:

phi= -0.7048                                 
z=rep(0,100)                                 
e=rnorm(n=100,0,0.345)                       
cons=2.1                                     
z[1]=4.1
for (i in 2:100) z[i]=cons+phi*z[i-1]+e[i]   
plot(ts(Y))

How do i include the difference term ARI(1,1) in above code.
Any one help me in this regard.

Best Answer

If you want to simulate ARIMA you can use arima.sim in R, there is no need to do it by hand. This will generate the series you want.

e <- rnorm(100,0,0.345) 
arima.sim(n=100,model=list(ar=-0.7048,order=c(1,1,0)),start.innov=4.1,n.start=1,innov=2.1+e)

You can look at the code of how this is achieved by typing arima.sim in R command line. Alternatively if you do it yourself, the function you are probably looking is diffinv. It computes the inverse of lagged differences.

For recursive sequences R has a nice function filter. So instead of using loop 

z <- rep(NA,100)
z[1] <- 4.1
for (i in 2:100) z[i]=cons+phi*z[i-1]+e[i]

you can write 

filter(c(4.1,2.1+e),filter=-0.7048,method="recursive")

This will give the identical result to arima.sim example above:

diffinv(filter(c(4.1,2.1+e),filter=-0.7048,method="recursive")[-1])
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