# [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]]
>     >
>     >
>     >
>     ------------------------------------------------------------------------
>     >
>     > _______________________________________________
>     > R-SIG-Finance at stat.math.ethz.ch
>     <mailto:R-SIG-Finance at stat.math.ethz.ch> mailing list
>     > https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>     > -- Subscriber-posting only.
>     > -- If you want to post, subscribe first.
>
>     _______________________________________________
>     R-SIG-Finance at stat.math.ethz.ch
>     <mailto:R-SIG-Finance at stat.math.ethz.ch> mailing list
>     https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>     -- Subscriber-posting only.
>     -- If you want to post, subscribe first.
>

```