From: Rolf Turner <rolf.turner_at_xtra.co.nz>

Date: Tue, 24 May 2011 10:03:29 +1200

R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Mon 23 May 2011 - 22:07:43 GMT

Date: Tue, 24 May 2011 10:03:29 +1200

On 24/05/11 01:24, user84 wrote:

*> Hi,
*

> could anyone tell me how predict() predicts the new value(s), of a MA(1)

*> arima-modell.
**> its really easy to make it with an AR(1), knowing the last term, but how can
**> i or R know the last error?
*

I think what you're asking here is this:

Suppose X_t = a_t + theta * a_{t-1} where {a_t} is ``white noise''. If you have observed X_1, ..., X_n, the ``prediction'' of X_{n+1} is theta * a_n, since E(a_{n+1}) = 0. But how do you get a_n? Recursively. Set a_0 = 0 (its expected value). This gives a_1 = X_1. Then you can get a_2 = X_2 - theta*a_1. Repeat until you get up to a_n.

This is all a bit naive, and there are traps and problems that are avoided by more sophisticated procedures, I believed.

A simple answer to the ``how to'' bit, is: Use predict.Arima().

If you want to know what's actually going on in the software that
makes this prediction .... that's a bit harder. I think that reading a
basic introductory time series book might help. Jonathan Cryer's
``Time Series Analysis'' (out of print but available from ABE Books)
is pretty good, and quite gentle. I suspect that the newer ``Time
Series Analysis with Applications in R'' by Cryer and Chan would also
be good, but I haven't read it. For something a bit deeper and
more mathematical, Brockwell and Davis (``Time Series: Theory
and Methods'') is to my mind the gold standard.

> It would also help if somebody could tell me how to find the "open" source

*> of the function predict().
*

Note that ``predict()'' is generic, with many ``methods''. You are really interested in the predict.Arima() method as I indicated above.

You can get started by executing:

stats:::predict.Arima

But that will lead you to KalmanForecast() which will lead you into C code.
You can look at *that* by downloading the source of R from CRAN and
digging around in the appropriate "src" subdirectories --- but figuring
out what's actually going on is likely to be a ***very*** daunting task.
I wouldn't want to try it myself!

> Thanks and sorry for my poor english.

No need to apologize. Your English is better than my Deutsch. (The ``.at'' address *does* mean ``Austria'', nicht wahr?)

**HTH
**
cheers,

Rolf Turner

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