[R-SIG-Finance] Problem with forecast se in the forecast package

[Adam Ginensky]

Hi,
I don't know what's going on, but notice the 'bad' sd estimates are
essentially double the 'correct' sd estimates.  There is likely a
connection.

Best,

Adam Ginensky

On Mon, Dec 26, 2016 at 7:19 AM, Ajay Shah <ajayshah at mayin.org> wrote:
> I was experimenting with the most impressive forecast package. I tried to
> rig up a simplest demo of auto.arima() in action. The forecast sd looks odd
> to me. Here's a demo.
>
> ## Reproducibility
> set.seed(101)
>
> ## Simulate a series from AR(1)
> x <- arima.sim(list(order = c(1,0,0), ar = 0.8), n = 1000)
> sd(x)
>   # This is 1.566 which seems right
>
> ## Using ar()
> m1 <- ar(x)
>
> ## Use forecast::auto.arima()
> library(forecast)
> m2 <- auto.arima(x)
>
> ## How did they fare?
> m1
> m2
>   # Both of them got the right model.
>
> f1 <- predict(m1, n.ahead=10)
> data.frame(pointest=as.numeric(f1$pred), sd=as.numeric(f1$se))
> f2 <- forecast(m2, h=10)
> data.frame(pointest=cbind(as.numeric(f2$mean),
> sd=(f2$upper[,2]-f2$lower[,2])/2))
>
> Let me show you the two results.
>
>> data.frame(pointest=as.numeric(f1$pred), sd=as.numeric(f1$se))
>      pointest        sd
> 1  -0.3186451 0.9628466
> 2  -0.2898804 1.2264023
> 3  -0.2671877 1.3649788
> 4  -0.2492853 1.4445294
> 5  -0.2351619 1.4918999
> 6  -0.2240198 1.5206374
> 7  -0.2152297 1.5382519
> 8  -0.2082952 1.5491136
> 9  -0.2028244 1.5558355
> 10 -0.1985085 1.5600043
>
> This seems right. The forecast sd is small at first, as we're exploiting
> the time series structure. But as we go deep into the future, the AR model
> is useless and we're down to the unconditional sd which is ~ 1.566.
>
>> f2 <- forecast(m2, h=10)
>> data.frame(pointest=cbind(as.numeric(f2$mean),
> sd=(f2$upper[,2]-f2$lower[,2])/2))
>    pointest.V1 pointest.sd
> 1  -0.28090691    1.887602
> 2  -0.22221139    2.406792
> 3  -0.17578030    2.681016
> 4  -0.13905100    2.839174
> 5  -0.10999628    2.933809
> 6  -0.08701255    2.991505
> 7  -0.06883127    3.027050
> 8  -0.05444897    3.049081
> 9  -0.04307186    3.062787
> 10 -0.03407199    3.071333
>
> This seems out of line. Right at n.ahead=1 the forecast sd is 1.8876 which
> is > 1.566. And going beyond, the forecast sd goes up to 3.07. What am I
> missing?
>
> --
> Ajay Shah
> ajayshah at mayin.org
> http://www.mayin.org/ajayshah
> http://ajayshahblog.blogspot.com
>
>         [[alternative HTML version deleted]]
>
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