[R-SIG-Finance] ARIMA(0,1,0)+c results estimate incorrect drift

[Nathan Bryant]

Hi,

I seem to have found a problem. Integrated ARIMA with drift uses a
linear regression on xreg and the results don't look numerically stable.
Forecasts are inconsistent with an equivalent arima(0,0,0) on
differenced data and with rwf. Maybe someone knows if there is a
rational explanation?

Try this,

library(forecast)
set.seed(3)
rand <- rnorm(1000, mean=.2)
mean(rand)
fit1 <- arima(diffinv(rand), order=c(0,1,0), include.drift=T)
coef(fit1)
fit2 <- arima(rand, order=c(0,0,0))
coef(fit2)



Without seed you may have to repeat the experiment a few times to see
the nuisance, seed is included to show an example of the problem:

> library(forecast)
> set.seed(3)
> rand <- rnorm(1000, mean=.2)
> mean(rand)
[1] 0.2063965
> fit1 <- arima(diffinv(rand), order=c(0,1,0), include.drift=T)
> coef(fit1)
    drift
0.2073960
> fit2 <- arima(rand, order=c(0,0,0))
> coef(fit2)
intercept
0.2063965




Nathan Bryant