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