standard error and p-value for the estimated parameter in AR model

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Hi

Yes dependance of regressor and errors has the effect that your 
estimator is biased. Hamilton (p 215) discusses the case of AR() with 
iid errors:

"the OLS coefficient gives a biased estimate in case of an autoregression 
and the standard t and F statistic can only be justified asymptotically. "

So as you point right out, normal distribution instead of student should 
be used for the p-values! (I'm not sure whether student distribution 
can't be used if you make the assumption that the errors are Gaussian. )

Note however that those results are derived for the OLS estimator, which 
is not the estimator by default in ar().

For small sample p-values, bootstrap methods could be used. Introductory 
discussion can be found in Maddala p 323 (available on google books, 
type: "the procedure for the generation of the bootstrap samples").

Matthieu

markleeds at verizon.net a ?crit :
hi matthew: maybe someone can say more including yourself but one 
doesn't have independence of error term
and regressor in an AR so I'm not certain that the t-test in the arima 
model is valid ?  I imagine that hamilton or
some other book must talk about the validity of the assumptions  but I 
don't have them in my apt at the moment.

On Jun 22, 2009, *Matthieu Stigler* <matthieu.stigler at gmail.com> wrote:

    Hi

    as you can see:

    methods(class="ar")

    there is no summary() nor confint() function for class ar :-(

    But if you check values returnd by ar:

    str(ar(lh))

    you see there is: asy.var.coef
    so with:

    sqrt(diag(ar(lh)$asy.var.coef))

    You get standard errors and can compute the corresponding p-values.

    Mat

    FMH a ?crit :
    > Dear All,
    >
    > I used an AR(1) model to explain the process of the stationary
    residual and have used an 'ar' command in R. From the results, i
    tried to extract the standard error and p-value for the estimated
    parameter, but unfortunately, i never find any way to extract it
    from the output.
    >
    > What i did was, i assigned the residuals into the 'residual'
    object in R and used an 'ar' function as below.
    >
    >
    >> residual <- residuals
    >> ar(residual, aic = TRUE, method = "mle", order.max = 1)
    >>
    >
    > Could someone help me to extract the stadard error and the
    p-value for the estimated parameter, please?
    >
    > Thank you
    >
    > Fir
    >
    >
    >
    > [[alternative HTML version deleted]]
    >
    >
    >
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