[R] test for arima coef's significancy

[Prof Brian Ripley]

On Mon, 8 Dec 2003, STOLIAROFF VINCENT wrote:

> Dear sirs, 
> 
> I would like to know if there is a function to compute the pvalue for the
> significancy of arima coef in an arima object created by 
> the arima function.
> 
> I have written this one:
> 
> pvalueArima<-function(x,arima)
> {
> t<-(arima$coef)/(diag(arima$var.coef)^0.5)
> df<-length(x)-length(arima$coef)
> 1-pt(t,df)
> }
> 
> Has somebody already implemented something equivalent ?

Can you explain how you managed to derive a t distribution for this 
statistic, yet none of the references mentioned in the various help pages 
contain such a result?

Could you also explain why a one-sided p-value is appropriate, and how the 
bounded space containing the coefficients is not relevant, nor are 
missing values in the series?

It's hard for the R-developers to write a function to compute something we 
do not know how to find theoretically, so please share your exceptional 
insights with us.

-- 
Brian D. Ripley,                  ripley at 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