[R-SIG-Finance] standard error and p-value for the estimated parameter in AR model
Matthieu Stigler
matthieu.stigler at gmail.com
Mon Jun 22 22:23:28 CEST 2009
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 écrit :
> 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 écrit :
> > 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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