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Re: best ARIMA model estimation

To: Wouter van Rijsinge <wprijsin@cs.uu.nl>
Subject: Re: best ARIMA model estimation
From: Prof Brian Ripley <ripley@stats.ox.ac.uk>
Date: Mon, 19 May 2003 10:36:01 +0100 (BST)
Cc: s-news@lists.biostat.wustl.edu
In-reply-to: <5.2.1.1.0.20030519093639.02497868@imaps.students.cs.uu.nl>
On Mon, 19 May 2003, Wouter van Rijsinge wrote:

> R 1.7.0 on Windows 2000

So this is not the appropriate list: R-help@r-project.org is.

> I try to estimate the 'best' ARIMA model for a time series (TS). The only 
> way I know to solve this problem is by brute force. 

There is a large literature on `model identification' in time series.

> Within 6 nested for 
> loops I try to get the best model based upon the Aikake Information 
> Criterion(aic).
> 
> A summary of the code:
> best.model <- arima(TS, order = c(1, 0, 0), seasonal = list(order = c(0, 0, 
> 0), period = frequency(TS)) )
> #And by brute force
> p, q, r, s are nested from 0 to 3 and i and j are nested from 0 to 2. p and 
> q are not both allowed to be 0.
>          # determine the best series
>          tmp <- arima(TS, order = c(p, i, q), seasonal = list(order = c(r, 
> j, s), period = frequency(TS)) )
>          if(best.model$aic > tmp$aic)
>          {
>                  best.model <- temp
>          }
> 
> Result:
> For a time series of 200 values it takes about 75 minutes to come up with 
> an answer and 50 warnings of the types:
> - NaNs produced in: log(x)
> - possible convergence problem: optim gave code= 1 in: arima(series, order 
> = c(p, i, q), seasonal = list(order = c(r,   ...
> 
> Questions
> 1. Is there a way to speed up the process (beside using a faster computer)?

No. You are fitting some seriously large seasonal arima models, many 
times.

> 2. How can I prevent the warnings from occurring occurring?

Be more careful to fit appropriate models (and to ask the appropriate 
list).

-- 
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595


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