# Convert prediction for differenced Time Series ARIMA(1,0,1) and ARIMA (1,1,1)

I am working on a Time Series model, and the series appeared to be non-stationary (presence of trend).

I tried 2 ways:

1) put original data into ARIMA(1,1,1)

2) manually difference first order data then put into ARIMA(1,0,1)

I thought after I convert back the 2) method prediction value, the value should be equal to the 1)one

But it turns out to be different as below.

Anyone know why?

(green is prediction value ARIMA(1,1,1), yellow is convert value from ARIMA(1,0,1)

# Without integrated term:

plot( forecast(Arima(y = WWWusage, order = c(1,0,1))) )

# With integrated term:

plot( forecast(Arima(y = WWWusage, order = c(1,1,1))) )

Predict:

• see robert stoffer's web page. I don't know if it's still there but he used to have a beautiful explanation of why this happens ( it's a problem with R ) and what to do about it. If you can't find it, let me know. He's at the university of pittsburgh. – mlofton Jul 6 at 2:44
• Actually, it looks like you're not using base R which I assumed you were using. Maybe there's a similar thing with whatever R package ( forecast package ? ) you're using so Stoffer's explanation may still be worth checking out. – mlofton Jul 6 at 2:46
• @mlofton I found the link. Thanks! – Wenyi Yan Jul 6 at 4:48
• great. I'm not sure if the R package you're using does the same thing as base R but Stoffer's explanation is quite nice. Good luck. – mlofton Jul 7 at 4:52