R devel - Nov 2002 - Prediction from arima() object (library ts) (PR#2305)

Full_Name: Allan McRae
Version: 1.6.0
OS: Win 2000 P
Submission from: (NULL) (129.215.190.229)


When using predict.Arima in library ts(), it appears differencing is only
accounted for in the first step of prediction and so any trend is not apparent
in the predictions.  The example shows the difference between the predictions of
an arima(1,1,1) model and the backtransformed predictions of an arima(1,0,1)
model fitted on the differenced data.

Example:

total <- c(750, 775, 971, 1099, 1344, 610, 910, 1056, 1589, 1006, 1469, 1598,
876, 1104, 1197, 1062, 1783, 1554, 1400, 1340, 1013, 1031, 1030, 860, 943, 1542,
1400, 1301, 1443, 1057, 1296, 710, 1038, 1447, 694, 889, 1459, 957, 1284, 1520,
1172, 1826, 1751, 1968, 933, 1409, 1889)

revtotal <- numeric(length(total))
for(i in 1:length(total))
	revtotal[i] <- total[length(total)-i+1]

# first model
m1 <- arima(revtotal, c(1,1,1))
pm1 <- predict(m1, n.ahead=15)
plot(1:47, y=revtotal, type="l", xlim=c(0,65))
lines(48:62, y=pm1$pred, col="red")

# second model - differencing done manually
drevtotal <- diff(revtotal)
m <- arima(drevtotal, c(1,0,1))
pm <- predict(m, n.ahead=15)
p <- numeric(15)
p[1] <- pm$pred[1] + revtotal[length(revtotal)]
for(i in 2:15)
	p[i] <- p[i-1] + pm$pred[i]
plot(1:47, y=revtotal, type="l", xlim=c(0,65))
lines(48:62, y=p, col="red")

Your `manual' code is misguided: I don't think you understand ARIMA
processes.

Read the help page more carefully, including the parameter `include.mean'.
If you use the correct differenced model, you will verify that arima is
working correctly.

Please don't report bugs unless you are sure you understand your own email
address!

On Mon, 18 Nov 2002 mcrae_allan@hotmial.com wrote:
                                ^^^^^^^  sic!
> Full_Name: Allan McRae
> Version: 1.6.0
> OS: Win 2000 P
> Submission from: (NULL) (129.215.190.229)
>
>
> When using predict.Arima in library ts(), it appears differencing is only
> accounted for in the first step of prediction and so any trend is not
apparent
> in the predictions.  The example shows the difference between the
predictions of
> an arima(1,1,1) model and the backtransformed predictions of an
arima(1,0,1)
> model fitted on the differenced data.
>
> Example:
>
> total <- c(750, 775, 971, 1099, 1344, 610, 910, 1056, 1589, 1006, 1469,
1598,
> 876, 1104, 1197, 1062, 1783, 1554, 1400, 1340, 1013, 1031, 1030, 860, 943,
1542,
> 1400, 1301, 1443, 1057, 1296, 710, 1038, 1447, 694, 889, 1459, 957, 1284,
1520,
> 1172, 1826, 1751, 1968, 933, 1409, 1889)
>
> revtotal <- numeric(length(total))
> for(i in 1:length(total))
> 	revtotal[i] <- total[length(total)-i+1]
>
> # first model
> m1 <- arima(revtotal, c(1,1,1))
> pm1 <- predict(m1, n.ahead=15)
> plot(1:47, y=revtotal, type="l", xlim=c(0,65))
> lines(48:62, y=pm1$pred, col="red")
>
> # second model - differencing done manually
> drevtotal <- diff(revtotal)
> m <- arima(drevtotal, c(1,0,1))
That line is incorrect.
> pm <- predict(m, n.ahead=15)
> p <- numeric(15)
> p[1] <- pm$pred[1] + revtotal[length(revtotal)]
> for(i in 2:15)
> 	p[i] <- p[i-1] + pm$pred[i]
> plot(1:47, y=revtotal, type="l", xlim=c(0,65))
> lines(48:62, y=p, col="red")
>
> ______________________________________________
> R-devel@stat.math.ethz.ch mailing list
> http://www.stat.math.ethz.ch/mailman/listinfo/r-devel
>
-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595