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

[hidden email]
http://www.mayin.org/ajayshahhttp://ajayshahblog.blogspot.com [[alternative HTML version deleted]]

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